Introduction

In our case study, we will explore the factors that can best predict air pollution in the United States, divided by regional zip codes. Air pollution causes more health problems for the overall public and the ecosystem of the United States than are accurately portrayed in the media. According to the State of Global Air [1], air pollution is the fifth leading cause of deaths in the entire world. Death by air pollution is more common than more commonly known risks such as malnutrition, alcohol, and overall physical health. Even more surprisingly, air pollution kills more people than malaria and road traffic accidents.

Though it may seem obvious that the United States is divided on how much their daily activities contribute to air pollution and, in turn, climate change. The Pew Research Center [2] found that 20% of Americans don’t think that they contribute to air pollution levels. Many academic journals state otherwise, such as the UCAR Center for Science [3], which says that air pollution is the direct cause of climate change, indicating that Americans don’t necessarily know there is a high chance that they contribute to air pollution every day. National Geographic [4] says that air pollution is all around us, in our car emissions, factories, aerosols, planes, smoking, wildfires, etc.

While the United States has shown overall improvements in air quality from previous years [5], as time goes on, more pollutants enter the atmosphere, meaning that air pollution is still a very serious threat to the well-being of the United States and globally. Without widespread air pollution monitoring, we continue to put ourselves at risk. When there are very minimal amounts of pollutant monitors in the US, much of the United States population could be suffering from extremely dangerous amounts of pollutants when some of the observations are overlapping their readings.

Our research question aims to address these issues: Can we predict US annual average air pollution concentrations at the granularity of zip code regional levels using a diverse set of predictors, including population density, urbanization, road density, satellite pollution data, and chemical modeling data? Predicting air pollution levels in our case study does more than just address a problem; it can actually be used to later influence county/zip code-wide policies on products and actions that cause pollution. And, of course, with better predictions, we can hopefully save lives in the long run.

Resources:

[1] Health Effects Institute. 2019. State of Global Air 2019, www.stateofglobalair.org

[2] Tyson, Alec. “Two-Thirds of Americans Think Government Should Do More on Climate.” Pew Research Center Science & Society, Pew Research Center, 23 June 2020, www.pewresearch.org/science/2020/06/23/two-thirds-of-americans-think-government-should-do-more-on-climate/#:~:text=Most%20U.S.%20adults%20think%20human,at%20all%20to%20climate%20change. Accessed 07 Dec. 2023.

[3] Education, UCAR Center for Science. “Center for Science Education.” Air Quality and Climate Change | Center for Science Education, scied.ucar.edu/learning-zone/air-quality/air-quality-and-climate-change#:~:text=Air%20pollution%20is%20causing%20the,can%20negatively%20impact%20air%20quality. Accessed 07 Dec. 2023. [4] “Air Pollution.” Education, education.nationalgeographic.org/resource/air-pollution/. Accessed 07 Dec. 2023.

[5] EPA, Environmental Protection Agency, gispub.epa.gov/air/trendsreport/2019/#home. Accessed 07 Dec. 2023.

Load packages

library(tidyverse)
library(dplyr)
library(ggplot2)
library(tidymodels)
library(yardstick)
library(parsnip)
library(pROC)
library(patchwork)
library(caret)
library(MLmetrics)
pm <- readr::read_csv(here::here("OCS_data", "data","raw", "pm25_data.csv"))
## Rows: 876 Columns: 50── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (3): state, county, city
## dbl (47): id, value, fips, lat, lon, CMAQ, zcta, zcta_area, zcta_pop, imp_a5...
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Question

Case Study 2 Prompt: Can we predict US annual average air pollution concentrations at the granularity of zip code regional levels using predictors such as data about population density, urbanization, road density, as well as, satellite pollution data and chemical modeling data?

This case study aims to explore the feasibility of predicting annual average air pollution concentrations in the United States at a granular level, specifically within zip code regional boundaries. By leveraging a diverse set of predictors including population density, urbanization metrics, road density, and integrating satellite pollution data along with chemical modeling information, the objective is to develop a comprehensive predictive model. This model could potentially offer insights into localized air quality variations, aiding in targeted interventions and policy-making efforts aimed at mitigating air pollution’s impact on public health and the environment.

Extension:

The Data

This dataset compiles diverse environmental and demographic information from monitoring stations across the United States. It includes air pollution estimates derived from a computational model (CMAQ), satellite-derived aerosol measurements (Aerosol Optical Depth), and emissions data from major sources within varying radii around monitoring sites. Additionally, it encompasses geographical details such as impervious surface measurements, road lengths, population densities, educational attainment percentages, poverty rates, and urban-rural classifications at the county and zip code levels. The dataset aims to offer a comprehensive view of potential predictors influencing air quality variations, allowing for granular analysis and prediction at localized levels like zip code areas, fostering insights valuable for targeted interventions and policy formulation to address air pollution concerns.

List of Features: id: Monitor number (county number before the decimal, monitor number after)

fips: Federal Information Processing Standard number for the county

Lat: Latitude of the monitor in degrees

Lon: Longitude of the monitor in degrees

state: State where the monitor is located

county: County where the monitor is located

city: City where the monitor is located

CMAQ: Estimated air pollution values from the Community Multiscale Air Quality model

zcta: Zip Code Tabulation Area where the monitor is located

zcta_area: Land area of the zip code area in square meters

zcta_pop: Population in the zip code area

imp_a500, imp_a1000, imp_a5000, imp_a10000, imp_a15000: Impervious surface measures within different radii around the monitor

county_area: Land area of the county of the monitor in square meters

county_pop: Population of the county of the monitor

Log_dist_to_prisec: Natural log distance to primary or secondary road from the monitor

log_pri_length_5000, log_pri_length_10000, log_pri_length_15000, log_pri_length_25000: Count of primary road length in meters within various radii around the monitor (Natural log)

log_prisec_length_500, log_prisec_length_1000, log_prisec_length_5000, log_prisec_length_10000, log_prisec_length_15000, log_prisec_length_25000: Count of primary and secondary road length in meters within various radii around the monitor (Natural log)

log_nei_2008_pm25_sum_10000, log_nei_2008_pm25_sum_15000, log_nei_2008_pm25_sum_25000: Tons of emissions from major sources within various radii around the monitor (Natural log)

log_nei_2008_pm10_sum_10000, log_nei_2008_pm10_sum_15000, log_nei_2008_pm10_sum_25000: Tons of emissions from major sources within various radii around the monitor (Natural log)

popdens_county: Population density of the county

popdens_zcta: Population density of the zip code area

nohs, somehs, hs, somecollege, associate, bachelor, grad: Educational attainment percentages in the zcta area

pov: Percentage of people in the zcta area living in poverty

hs_orless: Percentage of people in the zcta area with a high school degree or less

urc2013, urc2006: Urban-rural classification of the county

aod: Aerosol Optical Depth measurement from a NASA satellite, used as a proxy for particulate pollution

Data Import

pm <- read.csv("pm25_data.csv")
airports <- read.csv("airports2.csv")

Data Wrangling

pm |>
  glimpse()
## Rows: 876
## Columns: 50
## $ id                          <dbl> 1003.001, 1027.000, 1033.100, 1049.100, 10…
## $ value                       <dbl> 9.597647, 10.800000, 11.212174, 11.659091,…
## $ fips                        <int> 1003, 1027, 1033, 1049, 1055, 1069, 1073, …
## $ lat                         <dbl> 30.49800, 33.28126, 34.75878, 34.28763, 33…
## $ lon                         <dbl> -87.88141, -85.80218, -87.65056, -85.96830…
## $ state                       <chr> "Alabama", "Alabama", "Alabama", "Alabama"…
## $ county                      <chr> "Baldwin", "Clay", "Colbert", "DeKalb", "E…
## $ city                        <chr> "Fairhope", "Ashland", "Muscle Shoals", "C…
## $ CMAQ                        <dbl> 8.098836, 9.766208, 9.402679, 8.534772, 9.…
## $ zcta                        <int> 36532, 36251, 35660, 35962, 35901, 36303, …
## $ zcta_area                   <dbl> 190980522, 374132430, 16716984, 203836235,…
## $ zcta_pop                    <int> 27829, 5103, 9042, 8300, 20045, 30217, 901…
## $ imp_a500                    <dbl> 0.01730104, 1.96972318, 19.17301038, 5.782…
## $ imp_a1000                   <dbl> 1.4096021, 0.8531574, 11.1448962, 3.867647…
## $ imp_a5000                   <dbl> 3.3360118, 0.9851479, 15.1786154, 1.231141…
## $ imp_a10000                  <dbl> 1.9879187, 0.5208189, 9.7253870, 1.0316469…
## $ imp_a15000                  <dbl> 1.4386207, 0.3359198, 5.2472094, 0.9730444…
## $ county_area                 <dbl> 4117521611, 1564252280, 1534877333, 201266…
## $ county_pop                  <int> 182265, 13932, 54428, 71109, 104430, 10154…
## $ log_dist_to_prisec          <dbl> 4.648181, 7.219907, 5.760131, 3.721489, 5.…
## $ log_pri_length_5000         <dbl> 8.517193, 8.517193, 8.517193, 8.517193, 9.…
## $ log_pri_length_10000        <dbl> 9.210340, 9.210340, 9.274303, 10.409411, 1…
## $ log_pri_length_15000        <dbl> 9.630228, 9.615805, 9.658899, 11.173626, 1…
## $ log_pri_length_25000        <dbl> 11.32735, 10.12663, 10.15769, 11.90959, 12…
## $ log_prisec_length_500       <dbl> 7.295356, 6.214608, 8.611945, 7.310155, 8.…
## $ log_prisec_length_1000      <dbl> 8.195119, 7.600902, 9.735569, 8.585843, 9.…
## $ log_prisec_length_5000      <dbl> 10.815042, 10.170878, 11.770407, 10.214200…
## $ log_prisec_length_10000     <dbl> 11.88680, 11.40554, 12.84066, 11.50894, 12…
## $ log_prisec_length_15000     <dbl> 12.205723, 12.042963, 13.282656, 12.353663…
## $ log_prisec_length_25000     <dbl> 13.41395, 12.79980, 13.79973, 13.55979, 13…
## $ log_nei_2008_pm25_sum_10000 <dbl> 0.318035438, 3.218632928, 6.573127301, 0.0…
## $ log_nei_2008_pm25_sum_15000 <dbl> 1.967358961, 3.218632928, 6.581917457, 3.2…
## $ log_nei_2008_pm25_sum_25000 <dbl> 5.067308, 3.218633, 6.875900, 4.887665, 4.…
## $ log_nei_2008_pm10_sum_10000 <dbl> 1.35588511, 3.31111648, 6.69187313, 0.0000…
## $ log_nei_2008_pm10_sum_15000 <dbl> 2.26783411, 3.31111648, 6.70127741, 3.3500…
## $ log_nei_2008_pm10_sum_25000 <dbl> 5.628728, 3.311116, 7.148858, 5.171920, 4.…
## $ popdens_county              <dbl> 44.265706, 8.906492, 35.460814, 35.330814,…
## $ popdens_zcta                <dbl> 145.716431, 13.639555, 540.887040, 40.7189…
## $ nohs                        <dbl> 3.3, 11.6, 7.3, 14.3, 4.3, 5.8, 7.1, 2.7, …
## $ somehs                      <dbl> 4.9, 19.1, 15.8, 16.7, 13.3, 11.6, 17.1, 6…
## $ hs                          <dbl> 25.1, 33.9, 30.6, 35.0, 27.8, 29.8, 37.2, …
## $ somecollege                 <dbl> 19.7, 18.8, 20.9, 14.9, 29.2, 21.4, 23.5, …
## $ associate                   <dbl> 8.2, 8.0, 7.6, 5.5, 10.1, 7.9, 7.3, 8.0, 4…
## $ bachelor                    <dbl> 25.3, 5.5, 12.7, 7.9, 10.0, 13.7, 5.9, 17.…
## $ grad                        <dbl> 13.5, 3.1, 5.1, 5.8, 5.4, 9.8, 2.0, 8.7, 2…
## $ pov                         <dbl> 6.1, 19.5, 19.0, 13.8, 8.8, 15.6, 25.5, 7.…
## $ hs_orless                   <dbl> 33.3, 64.6, 53.7, 66.0, 45.4, 47.2, 61.4, …
## $ urc2013                     <int> 4, 6, 4, 6, 4, 4, 1, 1, 1, 1, 1, 1, 1, 2, …
## $ urc2006                     <int> 5, 6, 4, 5, 4, 4, 1, 1, 1, 1, 1, 1, 1, 2, …
## $ aod                         <dbl> 37.36364, 34.81818, 36.00000, 33.08333, 43…
skimr::skim(pm)
Data summary
Name pm
Number of rows 876
Number of columns 50
_______________________
Column type frequency:
character 3
numeric 47
________________________
Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
state 0 1 4 20 0 49 0
county 0 1 3 20 0 471 0
city 0 1 4 48 0 607 0

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
id 0 1 26987.96 1.578761e+04 1003.00 13089.15 26132.00 39118.00 5.603910e+04 ▇▇▆▇▆
value 0 1 10.81 2.580000e+00 3.02 9.27 11.15 12.37 2.316000e+01 ▂▆▇▁▁
fips 0 1 26987.89 1.578763e+04 1003.00 13089.00 26132.00 39118.00 5.603900e+04 ▇▇▆▇▆
lat 0 1 38.48 4.620000e+00 25.47 35.03 39.30 41.66 4.840000e+01 ▁▃▅▇▂
lon 0 1 -91.74 1.496000e+01 -124.18 -99.16 -87.47 -80.69 -6.804000e+01 ▃▂▃▇▃
CMAQ 0 1 8.41 2.970000e+00 1.63 6.53 8.62 10.24 2.313000e+01 ▃▇▃▁▁
zcta 0 1 50890.29 2.778447e+04 1022.00 28788.25 48172.00 74371.00 9.920200e+04 ▅▇▇▅▇
zcta_area 0 1 183173481.91 5.425989e+08 15459.00 14204601.75 37653560.50 160041508.25 8.164821e+09 ▇▁▁▁▁
zcta_pop 0 1 24227.58 1.777216e+04 0.00 9797.00 22014.00 35004.75 9.539700e+04 ▇▇▃▁▁
imp_a500 0 1 24.72 1.934000e+01 0.00 3.70 25.12 40.22 6.961000e+01 ▇▅▆▃▂
imp_a1000 0 1 24.26 1.802000e+01 0.00 5.32 24.53 38.59 6.750000e+01 ▇▅▆▃▁
imp_a5000 0 1 19.93 1.472000e+01 0.05 6.79 19.07 30.11 7.460000e+01 ▇▆▃▁▁
imp_a10000 0 1 15.82 1.381000e+01 0.09 4.54 12.36 24.17 7.209000e+01 ▇▃▂▁▁
imp_a15000 0 1 13.43 1.312000e+01 0.11 3.24 9.67 20.55 7.110000e+01 ▇▃▁▁▁
county_area 0 1 3768701992.12 6.212830e+09 33703512.00 1116536297.50 1690826566.50 2878192209.00 5.194723e+10 ▇▁▁▁▁
county_pop 0 1 687298.44 1.293489e+06 783.00 100948.00 280730.50 743159.00 9.818605e+06 ▇▁▁▁▁
log_dist_to_prisec 0 1 6.19 1.410000e+00 -1.46 5.43 6.36 7.15 1.045000e+01 ▁▁▃▇▁
log_pri_length_5000 0 1 9.82 1.080000e+00 8.52 8.52 10.05 10.73 1.205000e+01 ▇▂▆▅▂
log_pri_length_10000 0 1 10.92 1.130000e+00 9.21 9.80 11.17 11.83 1.302000e+01 ▇▂▇▇▃
log_pri_length_15000 0 1 11.50 1.150000e+00 9.62 10.87 11.72 12.40 1.359000e+01 ▆▂▇▇▃
log_pri_length_25000 0 1 12.24 1.100000e+00 10.13 11.69 12.46 13.05 1.436000e+01 ▅▃▇▇▃
log_prisec_length_500 0 1 6.99 9.500000e-01 6.21 6.21 6.21 7.82 9.400000e+00 ▇▁▂▂▁
log_prisec_length_1000 0 1 8.56 7.900000e-01 7.60 7.60 8.66 9.20 1.047000e+01 ▇▅▆▃▁
log_prisec_length_5000 0 1 11.28 7.800000e-01 8.52 10.91 11.42 11.83 1.278000e+01 ▁▁▃▇▃
log_prisec_length_10000 0 1 12.41 7.300000e-01 9.21 11.99 12.53 12.94 1.385000e+01 ▁▁▃▇▅
log_prisec_length_15000 0 1 13.03 7.200000e-01 9.62 12.59 13.13 13.57 1.441000e+01 ▁▁▃▇▅
log_prisec_length_25000 0 1 13.82 7.000000e-01 10.13 13.38 13.92 14.35 1.523000e+01 ▁▁▃▇▆
log_nei_2008_pm25_sum_10000 0 1 3.97 2.350000e+00 0.00 2.15 4.29 5.69 9.120000e+00 ▆▅▇▆▂
log_nei_2008_pm25_sum_15000 0 1 4.72 2.250000e+00 0.00 3.47 5.00 6.35 9.420000e+00 ▃▃▇▇▂
log_nei_2008_pm25_sum_25000 0 1 5.67 2.110000e+00 0.00 4.66 5.91 7.28 9.650000e+00 ▂▂▇▇▃
log_nei_2008_pm10_sum_10000 0 1 4.35 2.320000e+00 0.00 2.69 4.62 6.07 9.340000e+00 ▅▅▇▇▂
log_nei_2008_pm10_sum_15000 0 1 5.10 2.180000e+00 0.00 3.87 5.39 6.72 9.710000e+00 ▂▃▇▇▂
log_nei_2008_pm10_sum_25000 0 1 6.07 2.010000e+00 0.00 5.10 6.37 7.52 9.880000e+00 ▁▂▆▇▃
popdens_county 0 1 551.76 1.711510e+03 0.26 40.77 156.67 510.81 2.682191e+04 ▇▁▁▁▁
popdens_zcta 0 1 1279.66 2.757490e+03 0.00 101.15 610.35 1382.52 3.041884e+04 ▇▁▁▁▁
nohs 0 1 6.99 7.210000e+00 0.00 2.70 5.10 8.80 1.000000e+02 ▇▁▁▁▁
somehs 0 1 10.17 6.200000e+00 0.00 5.90 9.40 13.90 7.220000e+01 ▇▂▁▁▁
hs 0 1 30.32 1.140000e+01 0.00 23.80 30.75 36.10 1.000000e+02 ▂▇▂▁▁
somecollege 0 1 21.58 8.600000e+00 0.00 17.50 21.30 24.70 1.000000e+02 ▆▇▁▁▁
associate 0 1 7.13 4.010000e+00 0.00 4.90 7.10 8.80 7.140000e+01 ▇▁▁▁▁
bachelor 0 1 14.90 9.710000e+00 0.00 8.80 12.95 19.22 1.000000e+02 ▇▂▁▁▁
grad 0 1 8.91 8.650000e+00 0.00 3.90 6.70 11.00 1.000000e+02 ▇▁▁▁▁
pov 0 1 14.95 1.133000e+01 0.00 6.50 12.10 21.22 6.590000e+01 ▇▅▂▁▁
hs_orless 0 1 47.48 1.675000e+01 0.00 37.92 48.65 59.10 1.000000e+02 ▁▃▇▃▁
urc2013 0 1 2.92 1.520000e+00 1.00 2.00 3.00 4.00 6.000000e+00 ▇▅▃▂▁
urc2006 0 1 2.97 1.520000e+00 1.00 2.00 3.00 4.00 6.000000e+00 ▇▅▃▂▁
aod 0 1 43.70 1.956000e+01 5.00 31.66 40.17 49.67 1.430000e+02 ▃▇▁▁▁
pm <- na.omit(pm)
names(pm)
##  [1] "id"                          "value"                      
##  [3] "fips"                        "lat"                        
##  [5] "lon"                         "state"                      
##  [7] "county"                      "city"                       
##  [9] "CMAQ"                        "zcta"                       
## [11] "zcta_area"                   "zcta_pop"                   
## [13] "imp_a500"                    "imp_a1000"                  
## [15] "imp_a5000"                   "imp_a10000"                 
## [17] "imp_a15000"                  "county_area"                
## [19] "county_pop"                  "log_dist_to_prisec"         
## [21] "log_pri_length_5000"         "log_pri_length_10000"       
## [23] "log_pri_length_15000"        "log_pri_length_25000"       
## [25] "log_prisec_length_500"       "log_prisec_length_1000"     
## [27] "log_prisec_length_5000"      "log_prisec_length_10000"    
## [29] "log_prisec_length_15000"     "log_prisec_length_25000"    
## [31] "log_nei_2008_pm25_sum_10000" "log_nei_2008_pm25_sum_15000"
## [33] "log_nei_2008_pm25_sum_25000" "log_nei_2008_pm10_sum_10000"
## [35] "log_nei_2008_pm10_sum_15000" "log_nei_2008_pm10_sum_25000"
## [37] "popdens_county"              "popdens_zcta"               
## [39] "nohs"                        "somehs"                     
## [41] "hs"                          "somecollege"                
## [43] "associate"                   "bachelor"                   
## [45] "grad"                        "pov"                        
## [47] "hs_orless"                   "urc2013"                    
## [49] "urc2006"                     "aod"
pm <- pm |>
  rename(
   ImpSrf_500m = imp_a500,
    ImpSrf_1000m = imp_a1000,
    ImpSrf_5000m = imp_a5000,
    ImpSrf_10000m = imp_a10000,
    ImpSrf_15000m = imp_a15000,
    CountyArea_m2 = county_area,
    CountyPop = county_pop,
    Log_Dist_PrscRd = log_dist_to_prisec,
    Log_PriRdLen_5000m = log_pri_length_5000,
    Log_PriRdLen_10000m = log_pri_length_10000,
    Log_PriRdLen_15000m = log_pri_length_15000,
    Log_PriRdLen_25000m = log_pri_length_25000,
    Log_PrscRdLen_500m = log_prisec_length_500,
    Log_PrscRdLen_1000m = log_prisec_length_1000,
    Log_PrscRdLen_5000m = log_prisec_length_5000,
    Log_PrscRdLen_10000m = log_prisec_length_10000,
    Log_PrscRdLen_15000m = log_prisec_length_15000,
    Log_PrscRdLen_25000m = log_prisec_length_25000,
    Log_NEI_PM25_Sum_10000m = log_nei_2008_pm25_sum_10000,
    Log_NEI_PM25_Sum_15000m = log_nei_2008_pm25_sum_15000,
    Log_NEI_PM25_Sum_25000m = log_nei_2008_pm25_sum_25000,
    Log_NEI_PM10_Sum_10000m = log_nei_2008_pm10_sum_10000,
    Log_NEI_PM10_Sum_15000m = log_nei_2008_pm10_sum_15000,
    Log_NEI_PM10_Sum_25000m = log_nei_2008_pm10_sum_25000
  )

names(pm)
##  [1] "id"                      "value"                  
##  [3] "fips"                    "lat"                    
##  [5] "lon"                     "state"                  
##  [7] "county"                  "city"                   
##  [9] "CMAQ"                    "zcta"                   
## [11] "zcta_area"               "zcta_pop"               
## [13] "ImpSrf_500m"             "ImpSrf_1000m"           
## [15] "ImpSrf_5000m"            "ImpSrf_10000m"          
## [17] "ImpSrf_15000m"           "CountyArea_m2"          
## [19] "CountyPop"               "Log_Dist_PrscRd"        
## [21] "Log_PriRdLen_5000m"      "Log_PriRdLen_10000m"    
## [23] "Log_PriRdLen_15000m"     "Log_PriRdLen_25000m"    
## [25] "Log_PrscRdLen_500m"      "Log_PrscRdLen_1000m"    
## [27] "Log_PrscRdLen_5000m"     "Log_PrscRdLen_10000m"   
## [29] "Log_PrscRdLen_15000m"    "Log_PrscRdLen_25000m"   
## [31] "Log_NEI_PM25_Sum_10000m" "Log_NEI_PM25_Sum_15000m"
## [33] "Log_NEI_PM25_Sum_25000m" "Log_NEI_PM10_Sum_10000m"
## [35] "Log_NEI_PM10_Sum_15000m" "Log_NEI_PM10_Sum_25000m"
## [37] "popdens_county"          "popdens_zcta"           
## [39] "nohs"                    "somehs"                 
## [41] "hs"                      "somecollege"            
## [43] "associate"               "bachelor"               
## [45] "grad"                    "pov"                    
## [47] "hs_orless"               "urc2013"                
## [49] "urc2006"                 "aod"

Analysis

Exploratory Data Analysis

There are 49 elements in the state column. This is because only the 48 states within the continental U.S. are included, as well as the District of Columbia.

pm %>% 
  distinct(state) 
##                   state
## 1               Alabama
## 2               Arizona
## 3              Arkansas
## 4            California
## 5              Colorado
## 6           Connecticut
## 7              Delaware
## 8  District Of Columbia
## 9               Florida
## 10              Georgia
## 11                Idaho
## 12             Illinois
## 13              Indiana
## 14                 Iowa
## 15               Kansas
## 16             Kentucky
## 17            Louisiana
## 18                Maine
## 19             Maryland
## 20        Massachusetts
## 21             Michigan
## 22            Minnesota
## 23          Mississippi
## 24             Missouri
## 25              Montana
## 26             Nebraska
## 27               Nevada
## 28        New Hampshire
## 29           New Jersey
## 30           New Mexico
## 31             New York
## 32       North Carolina
## 33         North Dakota
## 34                 Ohio
## 35             Oklahoma
## 36               Oregon
## 37         Pennsylvania
## 38         Rhode Island
## 39       South Carolina
## 40         South Dakota
## 41            Tennessee
## 42                Texas
## 43                 Utah
## 44              Vermont
## 45             Virginia
## 46           Washington
## 47        West Virginia
## 48            Wisconsin
## 49              Wyoming

Interestingly, when comparing monitors between San Diego County and Baltimore County, there are fewer monitors in San Diego. This is despite San Diego having a much larger county population and a much larger county area. This could be correlated to county population density, as the population density for Baltimore is significantly higher than that of San Diego.

pm %>% filter(city == "San Diego")
##         id    value fips      lat       lon      state    county      city
## 1 6073.001 11.30495 6073 32.83646 -117.1288 California San Diego San Diego
## 2 6073.101 13.74281 6073 32.70149 -117.1497 California San Diego San Diego
##       CMAQ  zcta zcta_area zcta_pop ImpSrf_500m ImpSrf_1000m ImpSrf_5000m
## 1 9.679734 92123  21148247    26823    56.96540     42.59862     29.75533
## 2 9.679734 92113  13647793    56066    62.73443     57.59321     38.41929
##   ImpSrf_10000m ImpSrf_15000m CountyArea_m2 CountyPop Log_Dist_PrscRd
## 1      29.90047      31.03464   10895120648   3095313        5.889929
## 2      33.50957      33.20612   10895120648   3095313        6.439666
##   Log_PriRdLen_5000m Log_PriRdLen_10000m Log_PriRdLen_15000m
## 1           11.77990            12.84633            13.49200
## 2           11.57337            12.79770            13.25116
##   Log_PriRdLen_25000m Log_PrscRdLen_500m Log_PrscRdLen_1000m
## 1            13.88062           7.925588            9.681314
## 2            13.79533           6.214608            8.828726
##   Log_PrscRdLen_5000m Log_PrscRdLen_10000m Log_PrscRdLen_15000m
## 1            11.86692             12.93122             13.59976
## 2            11.71745             12.94720             13.45715
##   Log_PrscRdLen_25000m Log_NEI_PM25_Sum_10000m Log_NEI_PM25_Sum_15000m
## 1             14.19471                6.701290                6.788967
## 2             14.00775                5.154103                6.171575
##   Log_NEI_PM25_Sum_25000m Log_NEI_PM10_Sum_10000m Log_NEI_PM10_Sum_15000m
## 1                6.902245                6.853830                6.949341
## 2                7.151224                5.371998                6.340358
##   Log_NEI_PM10_Sum_25000m popdens_county popdens_zcta  nohs somehs    hs
## 1                7.076172       284.1008     1268.332  2.30   4.60 22.60
## 2                7.313310       284.1008     4108.063 10.25   9.65 21.95
##   somecollege associate bachelor   grad    pov hs_orless urc2013 urc2006  aod
## 1        28.6      9.00    21.80 11.100  6.800     29.50       1       1 53.0
## 2        23.6     10.25    16.35  7.975 12.125     41.85       1       1 74.2
pm %>% filter(city == "Baltimore")
##      id    value  fips      lat       lon    state           county      city
## 1 24510 12.20417 24510 39.34056 -76.58222 Maryland Baltimore (City) Baltimore
## 2 24510 12.53158 24510 39.34465 -76.68538 Maryland Baltimore (City) Baltimore
## 3 24510 12.79009 24510 39.28777 -76.54686 Maryland Baltimore (City) Baltimore
## 4 24510 14.28625 24510 39.23278 -76.57972 Maryland Baltimore (City) Baltimore
## 5 24510 13.31776 24510 39.29773 -76.60460 Maryland Baltimore (City) Baltimore
##       CMAQ  zcta zcta_area zcta_pop ImpSrf_500m ImpSrf_1000m ImpSrf_5000m
## 1 10.94099 21251    461424      934    23.86332     24.40061     30.29091
## 2 10.94099 21215  17645223    60161    39.58910     36.68274     20.15881
## 3 10.94099 21224  24539976    49134    52.56747     42.72426     40.15900
## 4 10.94099 21226  25718732     7561    47.92993     52.78222     27.00408
## 5 10.94099 21202   4111039    22832    54.16609     60.98106     47.61408
##   ImpSrf_10000m ImpSrf_15000m CountyArea_m2 CountyPop Log_Dist_PrscRd
## 1      30.97307      24.00093     209643241    620961        6.290041
## 2      24.94368      20.92504     209643241    620961        4.896128
## 3      31.35098      24.34897     209643241    620961        6.029092
## 4      30.85959      24.50620     209643241    620961        6.053460
## 5      31.35133      26.10478     209643241    620961        6.327766
##   Log_PriRdLen_5000m Log_PriRdLen_10000m Log_PriRdLen_15000m
## 1           10.30081            12.46166            13.13467
## 2           10.61036            12.08638            13.06048
## 3           11.40118            12.52707            13.06208
## 4           11.40602            12.63250            13.28804
## 5           11.25765            12.49259            13.32613
##   Log_PriRdLen_25000m Log_PrscRdLen_500m Log_PrscRdLen_1000m
## 1            13.68658           6.214608            9.451706
## 2            13.71012           7.788901            9.099535
## 3            13.69727           7.212027            9.387663
## 4            13.80005           6.990040            8.780156
## 5            13.74749           6.214608            9.087255
##   Log_PrscRdLen_5000m Log_PrscRdLen_10000m Log_PrscRdLen_15000m
## 1            12.08663             13.60081             14.25590
## 2            11.87033             13.44102             14.10281
## 3            12.21872             13.62511             14.19648
## 4            12.12845             13.60566             14.29857
## 5            12.42890             13.60451             14.36452
##   Log_PrscRdLen_25000m Log_NEI_PM25_Sum_10000m Log_NEI_PM25_Sum_15000m
## 1             14.87934                5.054359                5.830902
## 2             14.94211                3.118629                5.103638
## 3             14.85238                7.213761                8.282681
## 4             14.93222                8.285675                8.291580
## 5             14.91886                5.093924                8.287900
##   Log_NEI_PM25_Sum_25000m Log_NEI_PM10_Sum_10000m Log_NEI_PM10_Sum_15000m
## 1                8.325895                5.672080                6.365952
## 2                8.318862                3.189317                5.720812
## 3                8.326663                7.682122                8.596778
## 4                8.324531                8.594286                8.603195
## 5                8.325156                5.699463                8.595958
##   Log_NEI_PM10_Sum_25000m popdens_county popdens_zcta nohs somehs   hs
## 1                8.639569       2961.989    2024.1687  0.0    0.0  0.0
## 2                8.626094       2961.989    3409.4780  6.6   16.6 32.8
## 3                8.640220       2961.989    2002.2024 13.1   14.5 26.6
## 4                8.637902       2961.989     293.9881  9.2   13.9 37.1
## 5                8.638950       2961.989    5553.8271  6.2   18.6 27.1
##   somecollege associate bachelor grad    pov hs_orless urc2013 urc2006      aod
## 1         0.0      71.4      0.0 28.6  3.525       0.0       1       1 53.50000
## 2        21.0       4.6     11.1  7.3 21.200      56.0       1       1 53.41667
## 3        15.4       3.6     15.6 11.1 15.900      54.2       1       1 78.60000
## 4        16.9       4.9     12.5  5.5  7.200      60.2       2       2 78.60000
## 5        15.5       3.1     15.1 14.3 28.800      51.9       1       1 73.81818

This plot measures the correlation between each variable in the dataset. This is important to because we want to know which variables are actually predictive. If there are variables that show little to no correlation, we should not need to consider them when we generate our model as they are unnecessary. In the following plot, dark blue equates to a strong positive correlation why dark red equates to a strong negative correlation. Relationships that are not very strong are represented with lighter shades of these colors.

We can see that there is very strong correlation between the variables related to impervious surface measure, including the totals. This seems to show that if the area within a 500 meter radius of a monitor has a lot of impervious surfaces, we can expect the area within up to a 15000 meter radius of the same monitor to have a lot of impervious surfaces. We can see the same kind of correlation with the lengths of roads (primary and primary + secondary) within various radii of the monitors. However, the totals don’t seem to have as strong of a correlation. There is also a strong correlation between the total emissions for coarse and fine particulate matter. If a monitor reports a high amount of emissions for coarse particulate matter, we can expect a high amount of emissions for fine particulate matter as well. This correlation applies for all measured radii around each monitor. We noticed negative correlations between measures for impervious surfaces and road lengths when compared with URC scores from both 2006 and 2013. This makes sense, as a higher URC scale indicates a rural environment, which would have less roads and impervious surfaces.

PM_cor <- cor(pm %>% dplyr::select_if(is.numeric))
corrplot::corrplot(PM_cor, tl.cex = 0.5)

With this plot, we are visualizing the strengths of correlations without regard to positivity or negativity.

corrplot::corrplot(abs(PM_cor), order = "hclust", tl.cex = 0.5, cl.lim = c(0, 1))
## Warning in text.default(pos.xlabel[, 1], pos.xlabel[, 2], newcolnames, srt =
## tl.srt, : "cl.lim" is not a graphical parameter
## Warning in text.default(pos.ylabel[, 1], pos.ylabel[, 2], newrownames, col =
## tl.col, : "cl.lim" is not a graphical parameter
## Warning in title(title, ...): "cl.lim" is not a graphical parameter

This group of scatterplots visualizes the correlations between impervious surface measures within the various radii around monitors from 500 meters to 15000 meters. The correlation between the 500 meters and 15000 meters is the weakest, at 0.594, although this number still indicates a positive correlation. The strongest correlation is between 500 meters and 1000 meters, at 0.973. Thus, we can see that impervious surfaces are strongly correlated when comparing any radius.

# we used GGally in a previous set of notes
# will need to install if you haven't yet
select(pm, contains("imp")) %>%
  GGally::ggpairs()
## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2

This group of scatterplots visualizes the correlations between total emissions of both coarse and fine particulate matter within the various radii around the monitors from 10000 meters to 25000 meters. The correlation between fine particulate matter at 25000 meters and coarse particulate matter at 10000 meters is the weakest, at 0.717, which is still quite strong, and positive. The strongest correlation is between fine particulate matter at 15000 meters and coarse particulate matter at 15000 meters, at 0.990. Thus, we can see that total emissions of both coarse and fine particulate matter are strongly correlated when comparing any radius, and have a much stronger overall correlation when compared to impervious surface measure.

select(pm, contains("nei")) %>%
  GGally::ggpairs()

This correlation plot visualizes the correlations between primary road lengths, primary and secondary road lengths, and the distances between the monitors to primary and secondary roads. We can see that the strongest positive correlations are between primary road length at 10000 meters and 15000 meters, and between primary and secondary road length at the same radii. The distance from monitors to primary and secondary roads is strongly negatively correlated with primary and secondary road lengths at radii of 500 and 1000 meters. Across the plot, we can see positive correlations between road length measures and negative correlations when we compare these to distances.

select(pm, contains("Rd")) %>%
  GGally::ggcorr(hjust = .85, size = 3,
       layout.exp=2, label = TRUE)

This group of scatterplots visualizes the correlations between total emissions of fine particulate matter within a radius of 10000 meters, county populations, population densities, primary road lengths within a radius of 10000 meters, and impervious surface measure within 10000 meters. The correlation between fine particulate matter and county population is the weakest, at 0.176, which indicates very little relationship. This means that raw population number at the county level is not necessarily predictive of total emissions in that ares. The strongest correlation is between primary road length and impervious surface measure, at 0.649, which makes sense since roads are impervious surfaces themselves. and if there are more roads, there are likely more buildings in the area along those roads.

pm %>%
select(Log_NEI_PM25_Sum_10000m, popdens_county, 
       Log_PriRdLen_10000m, ImpSrf_10000m, CountyPop) %>%
  GGally::ggpairs()

This group of scatterplots visualizes the correlations between the same variables as above, except that county populations and population densities have been converted to a logarithmic scale. Taking into account these changes, we can see that the relationships involving these changed variables have stronger correlations. Now the strongest correlation is between county population and population density, at 0.790. The weakest correlation is still between fine particulate matter and county population, but the strength has increased, at 0.377.

pm %>%
  mutate(log_popdens_county=log(popdens_county),
         log_pop_county = log(CountyPop)) %>%
  select(Log_NEI_PM25_Sum_10000m, log_popdens_county, 
       Log_PriRdLen_10000m, ImpSrf_10000m, log_pop_county) %>%
  GGally::ggpairs()

This set of visualizations plots the tons of pollution within a 10000 meter radius of the monitors in comparison to the amount of impervious surfaces within the same area. The graphs are color coded by the urban-rural classification of each monitor. The second graph is a facet wrap where the points are separated by URC value. Based on this visual, there seems to be little relation between the tons of pollution and the amount of impervious surfaces; high pollution exists in areas with few impervious surfaces as well as areas with many impervious surfaces. However, we can see that the urban-rural classification has a relation to the amount of impervious surfaces.

ggplot(pm, aes(x=ImpSrf_10000m, y=Log_NEI_PM25_Sum_10000m, color=urc2013)) + 
  geom_jitter()

ggplot(pm, aes(x=ImpSrf_10000m, y=Log_NEI_PM25_Sum_10000m, color=urc2013)) + 
  geom_jitter() +
  facet_wrap(~urc2013)

This set of visualizations plots the relationships between estimated CMAQ values and the percentage of the population with Bachelor’s degrees, the percentage of the population with at most high school degrees, population densities, and the amount of roads within a 10000 meter radius of the monitors. The first two graphs compare the estimated CMAQ values in areas with different education levels. They reveal that most monitors are in areas where the percentage of people with Bachelor’s degrees is less than 50%, while the distribution of percentages of people with at most high school degrees is much wider. In both of these graphs, we can see that monitors in urban areas generally have higher CMAQ values than those in rural areas.

ggplot(pm, aes(x=bachelor, y=CMAQ, color=urc2013)) + 
  geom_jitter()

ggplot(pm, aes(x=hs_orless, y=CMAQ, color=urc2013)) + 
  geom_jitter()

This graph compares CMAQ values to the amount of roads within a 10000 meter radius of the monitors. Here we see rural areas have less roads compared to urban areas, and the amount of pollution seems to vary more in areas with less roads than areas with more roads.

ggplot(pm, aes(x=Log_PrscRdLen_1000m, y=CMAQ, color=urc2013)) + 
  geom_jitter()

This set of visualizations plots each of these points by latitude and longitude, which reveals the relative locations of each monitor. The first graph simply shows where urban areas are and where rural areas are.

ggplot(pm, aes(x=lon, y=lat, color=urc2013)) + 
  geom_jitter()

This graph shows which areas have more tons of pollution within a 10000 meter radius of the monitors. Here, compared with the graph above, it seems most pollution is in more urban areas.

ggplot(pm, aes(x=lon, y=lat, color=Log_NEI_PM25_Sum_10000m)) + 
  geom_jitter() +
  scale_color_continuous(high = "#132B43", low = "#b9e4ff")

This graph demonstrates the air pollution concentrations per state, it is clear that some states such as California, New York, Texas, and Louisiana had the highest range of air pollution concentrations. We were interested if population density played a role in this concentration.

ggplot(pm, aes(x = state, y = CMAQ)) +
  geom_boxplot() +
  labs(x = "State", 
       y = "Air Pollution Concentrations (CMAQ)",
       title = "Distribution of Air Pollution Concentrations by State") + 
  theme(axis.text.x = element_text(angle = 90, hjust = 1))

The graph above demonstrates the population density between the states, and it is clear that highest population density correlates a decent amount to air pollution concentration, however there’s also some drastic differences as well such as due to the size of texas being so big, the air pollution concentration is high, but the population density is low, but new york is high for both variables.

ggplot(pm, aes(x = state, y = popdens_zcta)) +
  geom_bar(stat = "summary", fun = "mean", fill = "skyblue") +
  labs(x = "State", y = "Average Population Density",
       title = "Average Population Density by State") +
  theme(axis.text.x = element_text(angle = 90, hjust = 1))

These boxplots above show the variability and central tendencies of air pollution estimates (‘CMAQ’) across different classifications of urban-rural areas in 2013 and 2006. They highlight potential differences or similarities in pollution levels based on these urban-rural classifications. We can see similar CMAQ scores for each classification between 2006 and 2013, although the 75th percentile has noticeably increased for score 6 in 2013. And while the median was slightly lower for score 5 compared to score 6, they are now at nearly the same level.

boxplot_urc2013 <- ggplot(pm, aes(x = factor(urc2013), y = CMAQ)) +
  geom_boxplot(fill = "lightcoral") +
  labs(title = "Boxplot of CMAQ by URC 2013", x = "URC 2013", y = "CMAQ")

boxplot_urc2006 <- ggplot(pm, aes(x = factor(urc2006), y = CMAQ)) +
  geom_boxplot(fill = "lightyellow") +
  labs(title = "Boxplot of CMAQ by URC 2006", x = "URC 2006", y = "CMAQ")

boxplot_urc2013

boxplot_urc2006

Data Analysis

Here we are converting columns for id, fips and zcta into factors since these represent categorical variables. We also create a new variable that indicates whether a monitor is in a city or not in a city, which will make it easier to categorize each monitor. Then we split 2/3 of our data to be used for training the random forest model we will be generating later. The remaining 1/3 will be used for testing our model.

# Converting to factors as discussed last class
pm <- pm %>%
  dplyr::mutate(across(c(id, fips, zcta), as.factor)) 
pm <- pm %>%
  mutate(city = case_when(city == "Not in a city" ~ "Not in a city",
                          city != "Not in a city" ~ "In a city"))

set.seed(1234) # same seed as before
pm_split <-rsample::initial_split(data = pm, prop = 2/3)
train_pm <-rsample::training(pm_split)
test_pm <-rsample::testing(pm_split)

Here we write our recipe for pre-processing our training data by specifying which variables should be considered as predictors, and which should be considered the outcome. We also want to make sure that we specify the variables that should not considered as predictors, since they are simply used for identification purposes. These include the id and fips variables, which are identification for each monitor and each county, respectively. We also remove variables that are highly correlated and those with non-zero variance as these will impact the accuracy of our model.

RF_rec <- recipe(train_pm) %>%
    update_role(everything(), new_role = "predictor")%>%
    update_role(value, new_role = "outcome")%>%
    update_role(id, new_role = "id variable") %>%
    update_role("fips", new_role = "county id") %>%
    step_novel("state") %>%
    step_string2factor("state", "county", "city") %>%
    step_rm("county") %>%
    step_rm("zcta") %>%
    step_corr(all_numeric())%>%
    step_nzv(all_numeric())

Here we are setting the parameters for our model. We set the number of predictor variables that will be randomly sampled to 10 and the number of data points required for a node to be split further to 3. We set the modeling engine to randomForest and the mode of the model to regression, since we want our model to be a Random Forest that predicts our outcome variable.

# install.packages("randomForest")
RF_PM_model <- parsnip::rand_forest(mtry = 10, min_n = 3) %>% 
  set_engine("randomForest") %>%
  set_mode("regression")

RF_PM_model
## Random Forest Model Specification (regression)
## 
## Main Arguments:
##   mtry = 10
##   min_n = 3
## 
## Computational engine: randomForest

Now we create a workflow that will combine our pre-processing recipe with the model we created. Then, we fit this workflow to our training dataset.

RF_wflow <- workflows::workflow() %>%
  workflows::add_recipe(RF_rec) %>%
  workflows::add_model(RF_PM_model)

RF_wflow
## ══ Workflow ════════════════════════════════════════════════════════════════════
## Preprocessor: Recipe
## Model: rand_forest()
## 
## ── Preprocessor ────────────────────────────────────────────────────────────────
## 6 Recipe Steps
## 
## • step_novel()
## • step_string2factor()
## • step_rm()
## • step_rm()
## • step_corr()
## • step_nzv()
## 
## ── Model ───────────────────────────────────────────────────────────────────────
## Random Forest Model Specification (regression)
## 
## Main Arguments:
##   mtry = 10
##   min_n = 3
## 
## Computational engine: randomForest
RF_wflow_fit <- parsnip::fit(RF_wflow, data = train_pm)

RF_wflow_fit
## ══ Workflow [trained] ══════════════════════════════════════════════════════════
## Preprocessor: Recipe
## Model: rand_forest()
## 
## ── Preprocessor ────────────────────────────────────────────────────────────────
## 6 Recipe Steps
## 
## • step_novel()
## • step_string2factor()
## • step_rm()
## • step_rm()
## • step_corr()
## • step_nzv()
## 
## ── Model ───────────────────────────────────────────────────────────────────────
## 
## Call:
##  randomForest(x = maybe_data_frame(x), y = y, mtry = min_cols(~10,      x), nodesize = min_rows(~3, x)) 
##                Type of random forest: regression
##                      Number of trees: 500
## No. of variables tried at each split: 10
## 
##           Mean of squared residuals: 2.633327
##                     % Var explained: 59.29

This code allows us to see the top 10 most important features in making predictions. We can see that state is the most important feature by a large margin compared to the second most important feature, which is CMAQ. Total emissions for coarse particulate matter within radii from 10000 to 25000 meters are also important predictors to keep in mind.

RF_wflow_fit %>% 
  extract_fit_parsnip() %>% 
  vip::vip(num_features = 10)

Here we perform a v-fold cross-validation with 4 folds using our training data. Then we tune our Random Forest workflow by training the model on subsets of our training data as defined by the cross-validation folds. Afterward, we collect the performance metrics from the tuned model. Our R-squared is 0.6, which indicates pretty good fit as it is closer to 1 than it is to 0.

set.seed(1234)
vfold_pm <- rsample::vfold_cv(data = train_pm, v = 4)
set.seed(456)
resample_RF_fit <- tune::fit_resamples(RF_wflow, vfold_pm)
collect_metrics(resample_RF_fit)
## # A tibble: 2 × 6
##   .metric .estimator  mean     n std_err .config             
##   <chr>   <chr>      <dbl> <int>   <dbl> <chr>               
## 1 rmse    standard   1.67      4  0.101  Preprocessor1_Model1
## 2 rsq     standard   0.591     4  0.0514 Preprocessor1_Model1

We will create a tuned model which will decide the number of predictor variables that will be randomly sampled and the number of data points required for a node to be split further for us. We set our model engine to randomForest and the mode to regression like before.

tune_RF_model <- rand_forest(mtry = tune(), min_n = tune()) %>%
  set_engine("randomForest") %>%
  set_mode("regression")
    
tune_RF_model
## Random Forest Model Specification (regression)
## 
## Main Arguments:
##   mtry = tune()
##   min_n = tune()
## 
## Computational engine: randomForest

We create a new workflow that uses our tuned model.

RF_tune_wflow <- workflows::workflow() %>%
  workflows::add_recipe(RF_rec) %>%
  workflows::add_model(tune_RF_model)

RF_tune_wflow
## ══ Workflow ════════════════════════════════════════════════════════════════════
## Preprocessor: Recipe
## Model: rand_forest()
## 
## ── Preprocessor ────────────────────────────────────────────────────────────────
## 6 Recipe Steps
## 
## • step_novel()
## • step_string2factor()
## • step_rm()
## • step_rm()
## • step_corr()
## • step_nzv()
## 
## ── Model ───────────────────────────────────────────────────────────────────────
## Random Forest Model Specification (regression)
## 
## Main Arguments:
##   mtry = tune()
##   min_n = tune()
## 
## Computational engine: randomForest

We detect how many CPU cores we have access to.

n_cores <- parallel::detectCores()
n_cores
## [1] 32

We can do parallel processing with that number of cores. We perform hyperparameter tuning on our new workflow and perform resampling with our previously created v-fold cross validation object. A grid search will be performed with 20 different combinations of hyperparameters. The goal here is to find which combination of hyperparameters will optimize our model’s performance.

# install.packages("doParallel")
doParallel::registerDoParallel(cores = n_cores)

set.seed(123)
tune_RF_results <- tune_grid(object = RF_tune_wflow, resamples = vfold_pm, grid = 20)
## i Creating pre-processing data to finalize unknown parameter: mtry

Looking at the results of our hyperparameter tuning, the best number of predictor variables to be randomly sampled is 32 and the best number of data points to be required for a node to be split further is 11.

tune_RF_results
## Warning: This tuning result has notes. Example notes on model fitting include:
## preprocessor 1/1, model 15/20: 36 columns were requested but there were 35 predictors in the data. 35 will be used.
## # Tuning results
## # 4-fold cross-validation 
## # A tibble: 4 × 4
##   splits            id    .metrics          .notes          
##   <list>            <chr> <list>            <list>          
## 1 <split [438/146]> Fold1 <tibble [40 × 6]> <tibble [0 × 1]>
## 2 <split [438/146]> Fold2 <tibble [40 × 6]> <tibble [0 × 1]>
## 3 <split [438/146]> Fold3 <tibble [40 × 6]> <tibble [1 × 1]>
## 4 <split [438/146]> Fold4 <tibble [40 × 6]> <tibble [0 × 1]>
tune_RF_results %>%
  collect_metrics()
## # A tibble: 40 × 8
##     mtry min_n .metric .estimator  mean     n std_err .config              
##    <int> <int> <chr>   <chr>      <dbl> <int>   <dbl> <chr>                
##  1    12    33 rmse    standard   1.72      4  0.0866 Preprocessor1_Model01
##  2    12    33 rsq     standard   0.562     4  0.0466 Preprocessor1_Model01
##  3    27    35 rmse    standard   1.69      4  0.102  Preprocessor1_Model02
##  4    27    35 rsq     standard   0.563     4  0.0511 Preprocessor1_Model02
##  5    22    40 rmse    standard   1.71      4  0.106  Preprocessor1_Model03
##  6    22    40 rsq     standard   0.556     4  0.0543 Preprocessor1_Model03
##  7     1    27 rmse    standard   2.03      4  0.0501 Preprocessor1_Model04
##  8     1    27 rsq     standard   0.440     4  0.0245 Preprocessor1_Model04
##  9     6    32 rmse    standard   1.77      4  0.0756 Preprocessor1_Model05
## 10     6    32 rsq     standard   0.552     4  0.0435 Preprocessor1_Model05
## # ℹ 30 more rows
show_best(tune_RF_results, metric = "rmse", n = 1)
## # A tibble: 1 × 8
##    mtry min_n .metric .estimator  mean     n std_err .config              
##   <int> <int> <chr>   <chr>      <dbl> <int>   <dbl> <chr>                
## 1    32    11 rmse    standard    1.65     4   0.113 Preprocessor1_Model10

Now that we know the best combination of parameters to use, we can finalize our workflow to use the tuned hyperparameter values. We then fit our finalized Random Forest model to both the training dataset and the testing dataset. We can see similar results for root mean squared and R squared between this finalized model and our previous results.

tuned_RF_values<- select_best(tune_RF_results, "rmse")
tuned_RF_values
## # A tibble: 1 × 3
##    mtry min_n .config              
##   <int> <int> <chr>                
## 1    32    11 Preprocessor1_Model10
# specify best combination from tune in workflow
RF_tuned_wflow <-RF_tune_wflow %>%
  tune::finalize_workflow(tuned_RF_values)

# fit model with those parameters on train AND test
overallfit <- RF_wflow %>%
  tune::last_fit(pm_split)

collect_metrics(overallfit)
## # A tibble: 2 × 4
##   .metric .estimator .estimate .config             
##   <chr>   <chr>          <dbl> <chr>               
## 1 rmse    standard       1.72  Preprocessor1_Model1
## 2 rsq     standard       0.610 Preprocessor1_Model1

We can see that our model predicts the values fairly accurately as the differences between most of the predicted values and actual values are quite small.

test_predictions <- collect_predictions(overallfit)
test_predictions
## # A tibble: 292 × 5
##    id               .pred  .row value .config             
##    <chr>            <dbl> <int> <dbl> <chr>               
##  1 train/test split  12.0     3  11.2 Preprocessor1_Model1
##  2 train/test split  11.6     5  12.4 Preprocessor1_Model1
##  3 train/test split  11.0     6  10.5 Preprocessor1_Model1
##  4 train/test split  13.3     7  15.6 Preprocessor1_Model1
##  5 train/test split  12.0     8  12.4 Preprocessor1_Model1
##  6 train/test split  10.6     9  11.1 Preprocessor1_Model1
##  7 train/test split  11.1    14  11.8 Preprocessor1_Model1
##  8 train/test split  11.1    16  10.0 Preprocessor1_Model1
##  9 train/test split  11.6    18  12.0 Preprocessor1_Model1
## 10 train/test split  12.0    20  13.2 Preprocessor1_Model1
## # ℹ 282 more rows
pm$row_indices <- seq_len(nrow(pm))
test_predictions$row_indices <- test_predictions$.row

# Merge the datasets using the row indices
merged_data <- merge(pm, test_predictions, by = "row_indices", all.x = TRUE)

cleaned_data <- merged_data[!is.na(merged_data$.row), ]
cleaned_data
##     row_indices       id.x   value.x  fips      lat        lon
## 3             3  1033.1002 11.212174  1033 34.75878  -87.65056
## 5             5   1055.001 12.375394  1055 33.99375  -85.99107
## 6             6  1069.0003 10.508850  1069 31.22636  -85.39077
## 7             7  1073.0023 15.591017  1073 33.55306  -86.81500
## 8             8  1073.1005 12.399355  1073 33.33111  -87.00361
## 9             9  1073.1009 11.103704  1073 33.45972  -87.30556
## 14           14  1073.5003 11.775000  1073 33.80167  -86.94250
## 16           16  1097.0003 10.032110  1097 30.76994  -88.08753
## 18           18  1101.0007 11.997867  1101 32.42583  -86.28528
## 20           20  1113.0001 13.163146  1113 32.47220  -85.00510
## 24           24  1127.0002 11.705833  1127 33.83278  -87.27250
## 26           26  4003.1005  6.911111  4003 31.34920 -109.53968
## 27           27  4005.1008  5.928814  4005 35.20611 -111.65278
## 28           28  4013.0019 10.492617  4013 33.48385 -112.14257
## 33           33     4015.1  5.528205  4015 35.54002 -113.41078
## 37           37  4021.3002  7.465179  4021 33.42119 -111.50322
## 42           42  5001.0011 11.249704  5001 34.51852  -91.55896
## 44           44  5035.0005 11.714754  5035 35.19729  -90.19314
## 46           46  5051.0003 11.153097  5051 34.46944  -93.00018
## 47           47  5067.0001 11.186885  5067 35.63729  -91.18891
## 48           48  5107.0001 11.058974  5107 34.52977  -90.58605
## 50           50  5115.0003 11.259322  5115 35.25977  -93.10005
## 52           52  5119.1004 12.119167  5119 34.72960  -92.24359
## 56           56  5143.0005 10.685088  5143 36.17970  -94.11683
## 62           62  6009.0001 10.164062  6009 38.20185 -120.68157
## 65           65  6019.0008 18.677009  6019 36.78133 -119.77319
## 68           68  6023.1002  7.600000  6023 40.80178 -124.16210
## 69           69  6023.1004  8.217241  6023 40.77694 -124.17750
## 72           72  6025.1003  8.082407  6025 32.79222 -115.56306
## 73           73  6027.1003  6.695946  6027 36.48782 -117.87104
## 78           78  6029.0016 23.160784  6029 35.32293 -118.99917
## 80           80  6033.3001  9.030159  6033 39.03270 -122.92229
## 81           81  6037.0002 14.213396  6037 34.13650 -117.92391
## 82           82  6037.1002 13.929661  6037 34.17605 -118.31712
## 89           89  6037.4004 13.709169  6037 33.79236 -118.17533
## 90           90  6037.9033  7.120000  6037 34.67139 -118.13146
## 92           92   6047.251 16.694872  6047 37.30854 -120.48099
## 93           93  6053.1003  7.166197  6053 36.69676 -121.63718
## 94           94  6057.0005 14.300000  6057 39.23433 -121.05659
## 96           96  6059.0007 12.765789  6059 33.83062 -117.93845
## 99           99  6063.1006 15.281356  6063 39.93710 -120.93882
## 109         109  6069.0002  6.936667  6069 36.84410 -121.36212
## 110         110  6071.0025 15.815044  6071 34.03722 -117.69000
## 111         111  6071.0306  8.644860  6071 34.51001 -117.33143
## 114         114  6071.9004 13.346847  6071 34.10688 -117.27411
## 115         115  6073.0001 12.305128  6073 32.63123 -117.05908
## 117         117  6073.0006 11.304951  6073 32.83646 -117.12875
## 119         119   6073.101 13.742812  6073 32.70149 -117.14965
## 129         129  6085.0005 12.265587  6085 37.34850 -121.89490
## 130         130  6087.0007  6.767213  6087 36.98392 -121.98933
## 134         134  6097.0003  9.078495  6097 38.44350 -122.71017
## 137         137  6107.2002 20.648092  6107 36.33218 -119.29123
## 139         139  6111.0009  9.693220  6111 34.40427 -118.80995
## 140         140  6111.2002 10.683193  6111 34.27636 -118.68376
## 144         144  8005.0005  7.184746  8005 39.60440 -105.01953
## 148         148  8031.0023  8.218750  8031 39.78108 -104.95665
## 151         151  8039.0001  4.318333  8039 39.23138 -104.63477
## 153         153  8069.0009  6.679167  8069 40.57129 -105.07969
## 154         154  8077.0017  9.112712  8077 39.06380 -108.56117
## 158         158   9001.001 11.921101  9001 41.17083  -73.19472
## 167         167  9009.0027 11.286893  9009 41.30140  -72.90287
## 172         172 10001.0002 11.368696 10001 38.98667  -75.55680
## 173         173 10001.0003 11.276786 10001 39.15500  -75.51806
## 175         175 10003.1007 11.484259 10003 39.55130  -75.73200
## 177         177 10003.2004 13.529223 10003 39.73944  -75.55806
## 180         180 11001.0042 12.436975 11001 38.87626  -77.03406
## 185         185 12009.0007  7.555372 12009 28.05361  -80.62861
## 193         193  12057.003  8.552956 12057 27.93194  -82.50972
## 196         196 12073.0012 10.567376 12073 30.43972  -84.34639
## 197         197 12086.0033  7.967826 12086 25.94194  -80.32639
## 200         200 12095.1004  7.545810 12095 28.55083  -81.34556
## 202         202 12099.0008  6.196026 12099 26.72444  -80.66667
## 209         209 12115.0013  6.931373 12115 27.29056  -82.50722
## 213         213 13051.0017 11.916340 13051 32.09296  -81.14399
## 217         217 13067.0003 13.743363 13067 34.01548  -84.60741
## 219         219 13089.0002 12.713120 13089 33.68797  -84.29048
## 220         220 13089.2001 13.073278 13089 33.90139  -84.27990
## 230         230 13215.0001 13.492857 13215 32.48354  -84.98098
## 232         232 13215.0011 13.163303 13215 32.42905  -84.93160
## 233         233 13223.0003 11.893966 13223 33.92850  -85.04534
## 236         236 13295.0002 12.475000 13295 34.97889  -85.30098
## 239         239  16001.001  7.912658 16001 43.60070 -116.34785
## 240         240 16001.0011  7.718627 16001 43.63611 -116.27028
## 242         242  16009.001  9.050442 16009 47.31667 -116.57028
## 244         244 16059.0004  9.720690 16059 45.18190 -113.89029
## 245         245 16079.0017 11.701630 16079 47.53639 -116.23667
## 246         246 17001.0007  9.181356 17001 39.91541  -91.33587
## 247         247 17019.0004 10.487931 17019 40.12380  -88.22953
## 253         253 17031.0076 11.905882 17031 41.75140  -87.71349
## 257         257 17031.3301 12.045378 17031 41.78277  -87.80538
## 261         261 17043.4002 11.291525 17043 41.77107  -88.15253
## 264         264 17089.0003 10.850000 17089 42.05040  -88.28002
## 266         266 17097.1007  9.360656 17097 42.46757  -87.81005
## 268         268 17111.0001 10.090090 17111 42.22144  -88.24221
## 273         273 17119.2009 12.410909 17119 38.90308  -90.14317
## 282         282 17197.1011 10.361667 17197 41.22154  -88.19097
## 283         283 17201.0013 10.709167 17201 42.26308  -89.09277
## 287         287 18037.0004 12.198000 18037 38.36944  -86.95903
## 288         288 18037.0005 12.535455 18037 38.40478  -86.92832
## 290         290 18039.0008 12.255856 18039 41.65691  -85.96837
## 300         300 18089.0031 12.227097 18089 41.59851  -87.34299
## 301         301 18089.2004 12.875653 18089 41.58550  -87.47449
## 304         304 18095.0009 12.184770 18095 40.11198  -85.67995
## 311         311 18141.0014 11.327500 18141 41.66346  -86.20783
## 312         312 18141.0015 12.376243 18141 41.69669  -86.21468
## 314         314 18157.0008 11.598977 18157 40.43164  -86.85250
## 315         315 18163.0006 12.266463 18163 37.97173  -87.56724
## 316         316 18163.0012 12.533333 18163 38.02173  -87.56946
## 317         317 18163.0016 12.453846 18163 37.97444  -87.53229
## 320         320 19013.0008 10.389916 19013 42.49306  -92.34389
## 322         322 19045.0021 10.997085 19045 41.87500  -90.17757
## 323         323 19055.0001 10.244444 19055 42.60083  -91.53849
## 325         325 19111.0008 11.435593 19111 40.40096  -91.39101
## 333         333 19155.0009 10.277391 19155 41.26417  -95.89612
## 336         336 19163.0019 13.464000 19163 41.51777  -90.61875
## 337         337 19177.0006  9.269643 19177 40.69508  -92.00632
## 339         339 19197.0004  9.154369 19197 42.69539  -93.65598
## 342         342 20107.0002  9.754545 20107 38.13588  -94.73199
## 351         351 21019.0017 12.074380 21019 38.45934  -82.64041
## 355         355 21047.0006 11.982051 21047 36.91171  -87.32334
## 356         356 21059.0005 12.016522 21059 37.78078  -87.07531
## 359         359 21073.0006 11.491597 21073 38.21936  -84.83850
## 360         360 21093.0006 12.231818 21093 37.70561  -85.85263
## 366         366 21117.0007 12.015702 21117 39.07250  -84.52500
## 368         368 21151.0003 10.459664 21151 37.73846  -84.28495
## 369         369 21183.0032 11.991667 21183 37.31972  -86.95610
## 370         370 21195.0002 10.552941 21195 37.48260  -82.53532
## 373         373 22019.0009  8.764078 22019 30.22778  -93.57833
## 374         374  22019.001  9.251887 22019 30.17714  -93.21451
## 376         376 22033.1001  9.660000 22033 30.59398  -91.25194
## 377         377 22047.0005 11.648113 22047 30.21910  -91.06255
## 385         385 22087.0007 10.584314 22087 29.94475  -89.97626
## 386         386 22105.0001 10.312587 22105 30.50306  -90.37694
## 391         391 24005.1007 11.709756 24005 39.46203  -76.63167
## 392         392 24005.3001 12.553754 24005 39.31083  -76.47444
## 393         393 24015.0003 13.223598 24015 39.70144  -75.86005
## 396         396 24033.0025 12.508772 24033 38.94121  -76.93219
## 401         401 24510.0007 12.531579 24510 39.34465  -76.68538
## 406         406 25005.1004  9.045902 25005 41.68571  -71.16924
## 407         407 25009.2006  8.713158 25009 42.47464  -70.97082
## 411         411 25013.0016 10.768908 25013 42.10899  -72.59080
## 412         412 25013.2009 10.809917 25013 42.10579  -72.59713
## 415         415 25025.0002 11.157018 25025 42.34887  -71.09716
## 416         416 25025.0027 10.668966 25025 42.37212  -71.06174
## 422         422 26017.0014  8.935088 26017 43.57139  -83.89072
## 423         423 26021.0014  9.898230 26021 42.19779  -86.30969
## 425         425 26033.0902 10.572500 26033 46.48167  -84.33167
## 435         435 26113.0001  6.522807 26113 44.31056  -84.89186
## 436         436 26115.0005 11.400855 26115 41.76389  -83.47194
## 437         437  26121.004  9.594253 26121 43.23306  -86.23858
## 438         438 26125.0001 10.895763 26125 42.46306  -83.18320
## 443         443 26163.0015 12.864754 26163 42.30279  -83.10653
## 446         446 26163.0025 10.958120 26163 42.42306  -83.42626
## 447         447 26163.0033 13.398319 26163 42.30667  -83.14875
## 451         451 27021.0001  4.744828 27021 47.15994  -94.15099
## 452         452  27037.047  9.490598 27037 44.73846  -93.23725
## 453         453 27053.0961  9.447500 27053 44.87551  -93.25892
## 458         458 27109.5008 10.176364 27109 43.99691  -92.45037
## 464         464 27137.7551  7.807563 27137 46.76643  -92.13354
## 467         467 27163.0446  8.405000 27163 45.02798  -92.77415
## 472         472 28043.0001 10.332174 28043 33.83444  -89.79278
## 473         473 28047.0008  9.804310 28047 30.39037  -89.04978
## 477         477 28075.0003 12.421849 28075 32.36456  -88.73149
## 483         483 29047.0005 10.109565 29047 39.30309  -94.37662
## 490         490 29510.0085 12.939266 29510 38.65650  -90.19865
## 492         492 29510.0093 13.363559 29510 38.65648  -90.18987
## 493         493 30013.1026  5.367213 30013 47.50222 -111.27889
## 494         494 30029.0007  8.893407 30029 48.38111 -114.17472
## 496         496 30029.0047  7.913115 30029 48.20054 -114.30533
## 503         503 30063.0021  7.850000 30063 47.17710 -113.48270
## 506         506 30089.0007  7.191964 30089 47.59439 -115.32375
## 507         507 30093.0005 10.190164 30093 46.00260 -112.50125
## 509         509 31055.0019  9.181564 31055 41.24749  -95.97314
## 514         514 31157.0003  6.783810 31157 41.86500 -103.66444
## 515         515 31177.0002  8.215534 31177 41.55121  -96.14617
## 516         516 32003.0561  9.284706 32003 36.16396 -115.11392
## 517         517 32003.1019  4.521622 32003 35.78567 -115.35705
## 524         524 33013.1006  8.712637 33013 43.13244  -71.45831
## 525         525 33015.0014  8.195082 33015 43.07533  -70.74800
## 527         527 34001.0006 10.230928 34001 39.46487  -74.44874
## 528         528 34001.1006 10.771875 34001 39.36326  -74.43100
## 532         532 34003.0009 12.334146 34003 40.83311  -74.04346
## 533         533 34007.0003 12.749593 34007 39.92304  -75.09762
## 535         535 34013.0015 12.957143 34013 40.73029  -74.21274
## 536         536 34015.0004 11.622936 34015 39.83081  -75.28472
## 549         549 34041.0006 11.166964 34041 40.69921  -75.18053
## 550         550 35001.0023  5.978932 35001 35.13430 -106.58520
## 553         553 35013.0017 12.436905 35013 31.79583 -106.55750
## 555         555 35017.1002  5.072381 35017 32.78444 -108.27167
## 556         556 35025.0008  6.211215 35025 32.72666 -103.12292
## 558         558 35045.0006  5.879747 35045 36.72750 -108.22083
## 559         559  35049.002  4.509322 35049 35.67111 -105.95361
## 566         566 36029.0005 10.692285 36029 42.87691  -78.80953
## 568         568 36031.0003  4.298276 36031 44.39308  -73.85890
## 575         575 36067.1015  8.150476 36067 43.05235  -76.05921
## 579         579 36085.0067 10.692308 36085 40.59664  -74.12525
## 581         581 36101.0003  7.913750 36101 42.09142  -77.20978
## 583         583 36119.1002 10.957143 36119 40.93149  -73.76575
## 589         589 37051.0009 12.348538 37051 35.04142  -78.95311
## 603         603 37117.0001 11.136134 37117 35.81066  -76.90625
## 604         604 37119.0041 12.395157 37119 35.24010  -80.78568
## 610         610 37147.0005 11.761538 37147 35.59417  -77.38611
## 611         611 37147.0006 11.853846 37147 35.63861  -77.35805
## 614         614 37173.0002 11.199145 37173 35.43477  -83.44213
## 616         616  37183.002 11.393043 37183 35.72880  -78.68020
## 617         617 37189.0003  9.153659 37189 36.22194  -81.66306
## 619         619 38007.0002  4.574138 38007 46.89430 -103.37853
## 621         621 38017.1004  8.327826 38017 46.93375  -96.85535
## 622         622 38057.0004  6.516129 38057 47.29861 -101.76694
## 625         625 39017.0016 13.789831 39017 39.33839  -84.56660
## 626         626 39023.0005 12.796581 39023 39.92882  -83.80949
## 628         628 39035.0027 13.222642 39035 41.48089  -81.70380
## 630         630 39035.0038 14.039241 39035 41.47701  -81.68238
## 631         631 39035.0045 13.638182 39035 41.47178  -81.65679
## 633         633 39035.0065 14.566102 39035 41.44668  -81.66242
## 636         636 39049.0025 12.441667 39049 39.92845  -82.98104
## 640         640 39061.0014 15.162147 39061 39.19433  -84.47897
## 650         650 39093.3002 11.372674 39093 41.46307  -82.11426
## 652         652 39095.0025 12.129268 39095 41.66579  -83.47611
## 653         653 39095.0026 12.345045 39095 41.62057  -83.64226
## 655         655 39099.0014 13.135294 39099 41.09594  -80.65852
## 657         657 39113.0032 13.359103 39113 39.76066  -84.18768
## 662         662  39151.002 12.450746 39151 40.80073  -81.37301
## 664         664 39153.0023 12.967544 39153 41.08796  -81.54161
## 669         669 40101.0169 11.555652 40101 35.75527  -95.37767
## 672         672 40115.9004  9.997414 40115 36.92222  -94.83889
## 674         674 40135.9015 11.084946 40135 35.58117  -94.83006
## 677         677  41017.012  5.221277 41017 44.06392 -121.31255
## 680         680 41029.1001  6.915517 41029 42.53611 -122.87500
## 684         684 41039.0058  8.422034 41039 44.06630 -123.13983
## 686         686 41039.1009  7.311290 41039 44.04670 -123.01770
## 689         689  41051.008  8.355085 41051 45.49664 -122.60288
## 690         690 41051.0246  7.737190 41051 45.56137 -122.66790
## 691         691 41059.0121  8.283193 41059 45.65223 -118.82303
## 692         692 41061.0119  6.715254 41061 45.33900 -118.09521
## 693         693 41067.0004  9.746154 41067 45.52850 -122.97240
## 694         694 42001.0001 11.427353 42001 39.92002  -77.30968
## 695         695 42003.0008 12.981311 42003 40.46542  -79.96076
## 698         698 42003.1008 13.518692 42003 40.61749  -79.72766
## 702         702 42011.0011 12.412931 42011 40.38335  -75.96860
## 703         703 42017.0012 12.533981 42017 40.10722  -74.88222
## 704         704 42021.0011 13.896721 42021 40.30972  -78.91500
## 705         705   42027.01 10.821448 42027 40.81139  -77.87703
## 709         709 42045.0002 13.870513 42045 39.83556  -75.37250
## 710         710 42049.0003 10.724633 42049 42.14175  -80.03861
## 711         711 42069.2006 10.077364 42069 41.44278  -75.62306
## 714         714 42091.0013 11.761468 42091 40.11222  -75.30917
## 715         715 42095.0025 12.267778 42095 40.62806  -75.34111
## 718         718 42101.0047 13.346515 42101 39.94465  -75.16521
## 720         720 42101.0057 13.094075 42101 39.96006  -75.14222
## 722         722   42125.02 12.380909 42125 40.17056  -80.26139
## 723         723 42125.5001 11.020625 42125 40.44528  -80.42083
## 725         725 42133.0008 13.402367 42133 39.96528  -76.69944
## 728         728 44007.0026 10.678632 44007 41.87467  -71.37997
## 730         730  44007.101  9.027193 44007 41.84157  -71.36077
## 734         734 45037.0001 12.163063 45037 33.73996  -81.85363
## 735         735 45041.0002 11.410909 45041 34.16764  -79.85040
## 741         741 45079.0007 12.383193 45079 34.09396  -80.96230
## 749         749 46071.0001  5.252941 46071 43.74561 -101.94122
## 752         752  46103.002  7.740496 46103 44.08740 -103.27378
## 753         753 46103.1001  6.715126 46103 44.07835 -103.22824
## 756         756 47065.4002 12.578903 47065 35.05092  -85.29302
## 759         759 48037.0004 11.167213 48037 33.42576  -94.07080
## 762         762  48113.005 11.487719 48113 32.77426  -96.79769
## 765         765 48135.0003  9.272131 48135 31.83657 -102.34204
## 768         768 48141.0044 11.859016 48141 31.76569 -106.45523
## 769         769 48141.0053 16.151786 48141 31.75853 -106.50105
## 770         770 48201.0024 11.776271 48201 29.90104  -95.32614
## 771         771 48201.0058 10.778947 48201 29.77070  -95.03123
## 785         785 49005.0004  9.704315 49005 41.73111 -111.83750
## 797         797 49057.1003  8.654310 49057 41.30361 -111.98787
## 800         800 50007.0012  7.759574 50007 44.48028  -73.21444
## 805         805 51041.0003 11.301639 51041 37.43467  -77.45118
## 807         807 51059.1005 11.229167 51059 38.83738  -77.16338
## 809         809  51069.001 12.063333 51069 39.28102  -78.08157
## 814         814 51165.0003 11.498198 51165 38.47753  -78.81952
## 815         815 51520.0006 10.589167 51520 36.60800  -82.16410
## 818         818 51710.0024 13.664641 51710 36.85555  -76.30135
## 820         820 51770.0015 11.701420 51770 37.29717  -79.95573
## 830         830 54003.0003 14.158261 54003 39.44801  -77.96412
## 837         837 54039.1005 14.201709 54039 38.36618  -81.69372
## 838         838 54049.0006 13.716379 54049 39.48148  -80.13467
## 843         843 54107.1002 13.856637 54107 39.32353  -81.55237
## 845         845 55009.0005 11.751882 55009 44.50729  -87.99344
## 851         851 55063.0012 11.835537 55063 43.77750  -91.22690
## 855         855 55079.0043 12.694958 55079 43.02641  -87.91111
## 856         856 55079.0059 13.318333 55079 42.95500  -87.93417
## 857         857 55079.0099 13.058333 55079 43.03987  -87.92079
## 859         859 55089.0009 11.272500 55089 43.49806  -87.81000
## 864         864 55133.0027 13.546400 55133 43.02007  -88.21507
## 870         870 56021.0001  4.500000 56021 41.13998 -104.81780
## 874         874 56035.0705  6.173494 56035 42.87053 -109.86096
##                    state               county          city      CMAQ  zcta
## 3                Alabama              Colbert     In a city  9.402679 35660
## 5                Alabama               Etowah     In a city  9.241744 35901
## 6                Alabama              Houston     In a city  9.121892 36303
## 7                Alabama            Jefferson     In a city 10.235612 35207
## 8                Alabama            Jefferson Not in a city 10.235612 35111
## 9                Alabama            Jefferson Not in a city  8.161789 35444
## 14               Alabama            Jefferson Not in a city  8.816101 35180
## 16               Alabama               Mobile     In a city  8.654895 36611
## 18               Alabama           Montgomery     In a city 10.219433 36110
## 20               Alabama              Russell     In a city  9.774144 31901
## 24               Alabama               Walker     In a city  8.140101 35501
## 26               Arizona              Cochise     In a city  5.266898 85626
## 27               Arizona             Coconino     In a city  5.108442 86011
## 28               Arizona             Maricopa     In a city 12.213530 85019
## 33               Arizona               Mohave     In a city  5.798753 86411
## 37               Arizona                Pinal     In a city 11.305553 85119
## 42              Arkansas             Arkansas     In a city 10.747275 72160
## 44              Arkansas           Crittenden     In a city 11.299191 72364
## 46              Arkansas              Garland     In a city  8.157882 71901
## 47              Arkansas              Jackson     In a city 13.111634 72112
## 48              Arkansas             Phillips     In a city 10.491194 72342
## 50              Arkansas                 Pope     In a city  8.728574 72801
## 52              Arkansas              Pulaski     In a city  9.915562 72202
## 56              Arkansas           Washington     In a city  8.270712 72764
## 62            California            Calaveras     In a city  7.442024 95249
## 65            California               Fresno     In a city  6.460891 93726
## 68            California             Humboldt     In a city  3.263085 95501
## 69            California             Humboldt     In a city  3.263085 95501
## 72            California             Imperial     In a city 14.850927 92243
## 73            California                 Inyo     In a city  3.513012 93530
## 78            California                 Kern     In a city  5.747609 93304
## 80            California                 Lake     In a city  3.106960 95453
## 81            California          Los Angeles     In a city 12.828002 91702
## 82            California          Los Angeles     In a city  9.270752 91502
## 89            California          Los Angeles     In a city  6.967713 90806
## 90            California          Los Angeles     In a city  7.908347 93534
## 92            California               Merced     In a city  6.814392 95348
## 93            California             Monterey     In a city  5.302320 93906
## 94            California               Nevada     In a city  6.999230 95945
## 96            California               Orange     In a city  9.799704 92804
## 99            California               Plumas     In a city  4.344805 95971
## 109           California           San Benito     In a city  6.855167 95045
## 110           California       San Bernardino     In a city 12.753308 91763
## 111           California       San Bernardino     In a city  9.821147 92395
## 114           California       San Bernardino     In a city 10.488258 92408
## 115           California            San Diego     In a city  7.145248 91911
## 117           California            San Diego     In a city  9.679734 92123
## 119           California            San Diego     In a city  9.679734 92113
## 129           California          Santa Clara     In a city  7.773003 95112
## 130           California           Santa Cruz     In a city  5.061995 95062
## 134           California               Sonoma     In a city  5.929803 95401
## 137           California               Tulare     In a city  6.584716 93292
## 139           California              Ventura     In a city  5.451476 93040
## 140           California              Ventura     In a city  6.898124 93063
## 144             Colorado             Arapahoe     In a city  4.573257 80120
## 148             Colorado               Denver     In a city  5.085550 80216
## 151             Colorado               Elbert Not in a city  4.932027 80106
## 153             Colorado              Larimer     In a city  3.848796 80521
## 154             Colorado                 Mesa     In a city  3.835828 81501
## 158          Connecticut            Fairfield     In a city  7.666388  6604
## 167          Connecticut            New Haven     In a city  8.597731  6513
## 172             Delaware                 Kent Not in a city  8.936072 19943
## 173             Delaware                 Kent     In a city  8.936072 19901
## 175             Delaware           New Castle Not in a city  9.750578 19701
## 177             Delaware           New Castle     In a city 10.006074 19801
## 180 District Of Columbia District of Columbia     In a city 10.379364 20024
## 185              Florida              Brevard     In a city  7.032766 32901
## 193              Florida         Hillsborough     In a city  9.425858 33609
## 196              Florida                 Leon     In a city 11.398163 32304
## 197              Florida           Miami-Dade     In a city  5.398935 33015
## 200              Florida               Orange     In a city 10.597919 32803
## 202              Florida           Palm Beach     In a city  9.015444 33430
## 209              Florida             Sarasota     In a city  7.769048 34231
## 213              Georgia              Chatham     In a city  8.573355 31408
## 217              Georgia                 Cobb     In a city  8.932246 30144
## 219              Georgia               DeKalb Not in a city 13.441151 30034
## 220              Georgia               DeKalb     In a city 13.441151 30341
## 230              Georgia             Muscogee     In a city  9.774144 31901
## 232              Georgia             Muscogee     In a city 11.067864 31903
## 233              Georgia             Paulding Not in a city  8.926431 30153
## 236              Georgia               Walker Not in a city  9.459333 30741
## 239                Idaho                  Ada Not in a city  4.777594 83642
## 240                Idaho                  Ada     In a city  4.777594 83704
## 242                Idaho              Benewah Not in a city  5.968979 83861
## 244                Idaho                Lemhi Not in a city  1.629838 83467
## 245                Idaho             Shoshone     In a city  3.762413 83839
## 246             Illinois                Adams     In a city  7.209795 62301
## 247             Illinois            Champaign     In a city  9.847546 61820
## 253             Illinois                 Cook     In a city 12.665990 60652
## 257             Illinois                 Cook     In a city 12.665990 60501
## 261             Illinois               DuPage     In a city 10.858659 60540
## 264             Illinois                 Kane     In a city 10.424477 60120
## 266             Illinois                 Lake     In a city 11.318619 60096
## 268             Illinois              McHenry     In a city  9.594218 60013
## 273             Illinois              Madison     In a city  9.167594 62002
## 282             Illinois                 Will     In a city  9.763484 60935
## 283             Illinois            Winnebago     In a city  8.366767 61104
## 287              Indiana               Dubois Not in a city 10.056619 47546
## 288              Indiana               Dubois     In a city 10.056619 47546
## 290              Indiana              Elkhart     In a city 10.677485 46516
## 300              Indiana                 Lake     In a city 16.909207 46402
## 301              Indiana                 Lake     In a city 16.909207 46323
## 304              Indiana              Madison     In a city 10.074651 46016
## 311              Indiana           St. Joseph     In a city 10.677485 46615
## 312              Indiana           St. Joseph     In a city 10.677485 46615
## 314              Indiana           Tippecanoe     In a city 10.383808 47904
## 315              Indiana          Vanderburgh     In a city 10.353399 47708
## 316              Indiana          Vanderburgh     In a city 10.353399 47710
## 317              Indiana          Vanderburgh     In a city 10.353399 47714
## 320                 Iowa           Black Hawk     In a city  7.031191 50703
## 322                 Iowa              Clinton     In a city  8.476871 52732
## 323                 Iowa             Delaware Not in a city  7.055311 52038
## 325                 Iowa                  Lee     In a city  7.147876 52632
## 333                 Iowa        Pottawattamie     In a city  7.267698 51510
## 336                 Iowa                Scott     In a city  8.892743 52802
## 337                 Iowa            Van Buren Not in a city  6.775811 52565
## 339                 Iowa               Wright     In a city  6.449447 50525
## 342               Kansas                 Linn Not in a city  7.091016 66075
## 351             Kentucky                 Boyd     In a city  9.249667 41101
## 355             Kentucky            Christian Not in a city  9.278928 42220
## 356             Kentucky              Daviess Not in a city 11.770804 42303
## 359             Kentucky             Franklin     In a city  9.463386 40601
## 360             Kentucky               Hardin     In a city  9.101351 42701
## 366             Kentucky               Kenton     In a city 11.791236 41011
## 368             Kentucky              Madison     In a city  9.471734 40475
## 369             Kentucky                 Ohio Not in a city  9.213426 42320
## 370             Kentucky                 Pike     In a city  9.442975 41501
## 373            Louisiana            Calcasieu     In a city 11.304278 70668
## 374            Louisiana            Calcasieu     In a city 13.328800 70601
## 376            Louisiana     East Baton Rouge Not in a city 14.006751 70807
## 377            Louisiana            Iberville Not in a city 15.346915 70721
## 385            Louisiana          St. Bernard     In a city  8.966612 70043
## 386            Louisiana           Tangipahoa     In a city  9.363830 70401
## 391             Maryland            Baltimore     In a city  9.634452 21030
## 392             Maryland            Baltimore     In a city 10.940985 21221
## 393             Maryland                Cecil Not in a city 12.053545 21921
## 396             Maryland      Prince George's     In a city 12.503977 20710
## 401             Maryland     Baltimore (City)     In a city 10.940985 21215
## 406        Massachusetts              Bristol     In a city  7.373641  2724
## 407        Massachusetts                Essex     In a city  8.038855  1904
## 411        Massachusetts              Hampden     In a city  6.457219  1103
## 412        Massachusetts              Hampden     In a city  6.457219  1103
## 415        Massachusetts              Suffolk     In a city  8.038855  2215
## 416        Massachusetts              Suffolk     In a city  8.038855  2129
## 422             Michigan                  Bay     In a city  8.184169 48708
## 423             Michigan              Berrien     In a city  7.698057 49038
## 425             Michigan             Chippewa     In a city  3.036035 49783
## 435             Michigan            Missaukee Not in a city  4.696748 49667
## 436             Michigan               Monroe     In a city  9.638580 48133
## 437             Michigan             Muskegon     In a city  5.980675 49440
## 438             Michigan              Oakland     In a city  8.680140 48237
## 443             Michigan                Wayne     In a city 10.164487 48209
## 446             Michigan                Wayne     In a city  8.680140 48152
## 447             Michigan                Wayne     In a city 10.164487 48120
## 451            Minnesota                 Cass Not in a city  3.737680 56641
## 452            Minnesota               Dakota     In a city  7.112881 55124
## 453            Minnesota             Hennepin     In a city  7.985953 55423
## 458            Minnesota              Olmsted     In a city  6.979581 55902
## 464            Minnesota          Saint Louis     In a city  3.939519 55806
## 467            Minnesota           Washington     In a city 12.591723 55003
## 472          Mississippi              Grenada     In a city  7.575577 38901
## 473          Mississippi             Harrison     In a city  8.637199 39507
## 477          Mississippi           Lauderdale     In a city  9.436430 39307
## 483             Missouri                 Clay Not in a city  7.626603 64068
## 490             Missouri       St. Louis City     In a city 12.080511 63107
## 492             Missouri       St. Louis City     In a city 12.080511 63102
## 493              Montana              Cascade     In a city  2.399152 59401
## 494              Montana             Flathead     In a city  2.362930 59912
## 496              Montana             Flathead     In a city  2.379521 59901
## 503              Montana             Missoula     In a city  2.370427 59868
## 506              Montana              Sanders     In a city  2.695437 59873
## 507              Montana           Silver Bow     In a city  1.890419 59703
## 509             Nebraska              Douglas     In a city  7.034605 68105
## 514             Nebraska         Scotts Bluff     In a city  3.899386 69361
## 515             Nebraska           Washington     In a city  7.034605 68008
## 516               Nevada                Clark     In a city  9.264662 89101
## 517               Nevada                Clark     In a city  8.390542 89179
## 524        New Hampshire            Merrimack     In a city  4.662478  3275
## 525        New Hampshire           Rockingham     In a city  4.859331  3904
## 527           New Jersey             Atlantic     In a city  8.857962  8205
## 528           New Jersey             Atlantic     In a city  8.857962  8401
## 532           New Jersey               Bergen     In a city 11.619372  7074
## 533           New Jersey               Camden     In a city 12.116203  8104
## 535           New Jersey                Essex     In a city  7.874637  7108
## 536           New Jersey           Gloucester     In a city 12.116203  8027
## 549           New Jersey               Warren     In a city  7.818637  8865
## 550           New Mexico           Bernalillo     In a city 10.102199 87109
## 553           New Mexico             Dona Ana Not in a city  7.813534 88063
## 555           New Mexico                Grant     In a city  5.302022 88022
## 556           New Mexico                  Lea     In a city  5.869165 88242
## 558           New Mexico             San Juan     In a city  5.917382 87401
## 559           New Mexico             Santa Fe     In a city  6.046069 87505
## 566             New York                 Erie     In a city  9.746405 14206
## 568             New York                Essex Not in a city  3.385406 12997
## 575             New York             Onondaga     In a city  5.595432 13214
## 579             New York             Richmond     In a city 11.619372 10314
## 581             New York              Steuben Not in a city  5.249962 14801
## 583             New York          Westchester     In a city  7.880172 10538
## 589       North Carolina           Cumberland     In a city  9.734499 28314
## 603       North Carolina               Martin     In a city  6.828791 27846
## 604       North Carolina          Mecklenburg     In a city  9.822602 28205
## 610       North Carolina                 Pitt     In a city  7.947334 27858
## 611       North Carolina                 Pitt Not in a city  7.947334 27834
## 614       North Carolina                Swain     In a city  6.331454 28713
## 616       North Carolina                 Wake Not in a city 10.097656 27606
## 617       North Carolina              Watauga     In a city  6.417602 28607
## 619         North Dakota             Billings Not in a city  2.756029 58622
## 621         North Dakota                 Cass Not in a city  4.833778 58102
## 622         North Dakota               Mercer Not in a city  3.585468 58523
## 625                 Ohio               Butler     In a city  9.781110 45015
## 626                 Ohio                Clark     In a city 10.913352 45503
## 628                 Ohio             Cuyahoga     In a city 10.372480 44113
## 630                 Ohio             Cuyahoga     In a city 10.372480 44113
## 631                 Ohio             Cuyahoga     In a city 10.372480 44127
## 633                 Ohio             Cuyahoga     In a city 10.372480 44105
## 636                 Ohio             Franklin     In a city 12.869319 43207
## 640                 Ohio             Hamilton     In a city 11.791236 45216
## 650                 Ohio               Lorain     In a city  8.595181 44054
## 652                 Ohio                Lucas     In a city 11.184033 43605
## 653                 Ohio                Lucas     In a city 11.184033 43614
## 655                 Ohio             Mahoning     In a city  8.409051 44503
## 657                 Ohio           Montgomery     In a city 10.668137 45402
## 662                 Ohio                Stark     In a city 10.896422 44702
## 664                 Ohio               Summit     In a city 10.896422 44320
## 669             Oklahoma             Muskogee     In a city  8.118360 74401
## 672             Oklahoma               Ottawa     In a city  7.169499 74360
## 674             Oklahoma             Sequoyah     In a city  7.784839 74962
## 677               Oregon            Deschutes     In a city  3.632990 97701
## 680               Oregon              Jackson     In a city  3.294533 97503
## 684               Oregon                 Lane     In a city  4.409401 97404
## 686               Oregon                 Lane     In a city  4.409401 97477
## 689               Oregon            Multnomah     In a city  5.704889 97206
## 690               Oregon            Multnomah     In a city  5.704889 97217
## 691               Oregon             Umatilla     In a city  2.716046 97801
## 692               Oregon                Union     In a city  2.314552 97850
## 693               Oregon           Washington     In a city  4.288868 97124
## 694         Pennsylvania                Adams Not in a city  8.188808 17353
## 695         Pennsylvania            Allegheny     In a city 10.517943 15224
## 698         Pennsylvania            Allegheny     In a city  8.420333 15065
## 702         Pennsylvania                Berks Not in a city  8.714116 19605
## 703         Pennsylvania                Bucks     In a city  9.168158 19007
## 704         Pennsylvania              Cambria     In a city  7.956593 15902
## 705         Pennsylvania               Centre     In a city  6.260422 16803
## 709         Pennsylvania             Delaware     In a city 10.092345 19013
## 710         Pennsylvania                 Erie     In a city  6.858108 16511
## 711         Pennsylvania           Lackawanna     In a city  6.267811 18519
## 714         Pennsylvania           Montgomery     In a city 12.116203 19401
## 715         Pennsylvania          Northampton     In a city  7.818637 18020
## 718         Pennsylvania         Philadelphia     In a city 12.116203 19147
## 720         Pennsylvania         Philadelphia     In a city 12.116203 19123
## 722         Pennsylvania           Washington     In a city  8.132669 15301
## 723         Pennsylvania           Washington Not in a city  9.569958 15021
## 725         Pennsylvania                 York     In a city 10.066116 17403
## 728         Rhode Island           Providence     In a city  7.373641  2860
## 730         Rhode Island           Providence     In a city  7.373641  2916
## 734       South Carolina            Edgefield Not in a city  9.171641 29847
## 735       South Carolina             Florence Not in a city  9.566813 29501
## 741       South Carolina             Richland     In a city 10.209979 29147
## 749         South Dakota              Jackson Not in a city  2.796456 57750
## 752         South Dakota           Pennington     In a city  3.111781 57702
## 753         South Dakota           Pennington     In a city  3.111781 57701
## 756            Tennessee             Hamilton     In a city  8.111289 37403
## 759                Texas                Bowie     In a city  8.901955 75501
## 762                Texas               Dallas     In a city 12.512475 75201
## 765                Texas                Ector     In a city  8.426707 79761
## 768                Texas              El Paso     In a city  7.315803 79905
## 769                Texas              El Paso     In a city  7.315803 79902
## 770                Texas               Harris     In a city 12.979706 77039
## 771                Texas               Harris     In a city 13.939939 77520
## 785                 Utah                Cache     In a city  3.533593 84321
## 797                 Utah                Weber     In a city  4.165049 84414
## 800              Vermont           Chittenden     In a city  5.117599  5401
## 805             Virginia         Chesterfield     In a city  8.145455 23234
## 807             Virginia              Fairfax     In a city 10.379364 22041
## 809             Virginia            Frederick Not in a city  8.590233 22624
## 814             Virginia           Rockingham Not in a city  6.754194 22802
## 815             Virginia         Bristol City     In a city  7.325804 24201
## 818             Virginia         Norfolk City     In a city  8.935473 23510
## 820             Virginia         Roanoke City     In a city  6.214850 24012
## 830        West Virginia             Berkeley     In a city  8.657932 25401
## 837        West Virginia              Kanawha     In a city  8.596698 25303
## 838        West Virginia               Marion     In a city  6.514602 26559
## 843        West Virginia                 Wood     In a city  9.496352 26105
## 845            Wisconsin                Brown     In a city  6.938970 54302
## 851            Wisconsin            La Crosse     In a city  7.227094 54601
## 855            Wisconsin            Milwaukee     In a city  8.759594 53204
## 856            Wisconsin            Milwaukee     In a city  8.759594 53221
## 857            Wisconsin            Milwaukee     In a city  8.759594 53203
## 859            Wisconsin              Ozaukee Not in a city  7.576285 53004
## 864            Wisconsin             Waukesha     In a city  8.759594 53186
## 870              Wyoming              Laramie     In a city  3.494108 82001
## 874              Wyoming             Sublette     In a city  2.377328 82941
##      zcta_area zcta_pop  ImpSrf_500m ImpSrf_1000m ImpSrf_5000m ImpSrf_10000m
## 3     16716984     9042 19.173010380 11.144896190  15.17861538    9.72538702
## 5    154069359    20045 16.493079580 11.096453290  14.67778782    8.22007849
## 6    162685124    30217 19.139273360 16.671496540  16.38548211    8.07396239
## 7     26929603     9010 41.833044980 41.032006920  36.00406256   23.17904127
## 8    166239542    16140  1.697653430  3.982392777   6.02132173    4.55677306
## 9    385566685     3699  0.000000000  0.029195502   0.13983563    0.14749677
## 14   230081840    13794  0.416089965  0.314878893   0.50526777    0.55436407
## 16    12304398     6106  4.415224913  7.137975779  10.88611101    8.61915436
## 18    76743399    12997 14.544982700 16.715830450  19.23057009   14.99611808
## 20    11526212     8638 60.453287200 49.143598620  25.78546970   16.35380485
## 24   129312323    10424  0.230968858  3.908520761   6.31025796    2.54823344
## 26     1907854     1021  2.191176471  6.884731834  21.31491739   34.12899364
## 27     1756314     6362 45.193771630 45.465353260  14.15930393    6.09215889
## 28     9712436    25042 42.699826990 47.867647060  46.96630799   42.57106226
## 33  1078691243      224  0.035467128  0.047577855   0.05337808    0.12004590
## 37   114040443    21219  9.136678201  6.527681661   4.72904838    5.19754611
## 42   870327339    10736  0.077854671  0.041738754   2.21037651    1.69591981
## 44   187833290    15831 19.891868510 19.809688580   7.01377240    5.83595233
## 46   267404865    29491 14.493944640 10.875648790  11.08313616    6.30600471
## 47   850468590    11467  0.121042831  0.438328466   1.33208764    1.45522827
## 48   231233559     5532  4.338447653  3.585860839   2.52292242    1.38636722
## 50    21061744    18685 34.968858130 30.480536330  12.05652210    4.89826289
## 52    22473183     9978 47.620242210 41.854831360  24.92685936   17.61485928
## 56   161282228    50230 37.698096890 35.264489620  19.88379077    9.23333752
## 62   217037743     4042  3.019400353  3.174809502   1.50897991    0.67654026
## 65    16619268    40705 49.064878890 45.014273360  43.17791961   40.84114189
## 68    18248993    23976 45.261245670 41.496539790  12.67844235    6.59641047
## 69    18248993    23976 43.503460210 39.262975780  12.62606878    6.79089928
## 72   285619001    48030 37.992214530 35.903330450  16.44853674    6.72002630
## 73     2362111       47  1.091695502  2.720588235   0.38475835    0.22145034
## 78    19670450    48731 41.965397920 43.215397920  32.53487838   24.70244922
## 80   216831467    11256  0.488754325  1.681228374   2.68808960    1.14045423
## 81   438640351    59705 39.298442910 40.727076120  33.99479185   31.15503477
## 82     3456372    11371 56.303633220 52.617647060  31.86506329   33.30081162
## 89     8908246    42399 52.006055360 54.985726640  47.85574061   44.81103720
## 90    45994950    39341 42.429065740 35.536764710  25.49895505   12.51693134
## 92   123033842    30805 34.037197230 29.309688580  18.68156800    7.08087441
## 93    33858896    59461 41.012975780 37.119593430  25.43141798    9.53441607
## 94   166352193    25199 12.400519030 21.561797750   7.28734735    2.30230859
## 96    18142648    85914 46.873702420 48.136031090  49.88297527   52.58511317
## 99   262028573     5970  0.000000000  0.000000000   2.00678758    0.69768383
## 109  122780227     4046  3.062283737  4.841695502   5.61140312    4.59982420
## 110   13393075    36375 25.130622840 23.440095160  38.03329100   30.35412187
## 111   44293390    42400 37.981833910 37.357482700  20.56785205   14.58713437
## 114   27507391    15271 31.811418690 31.540873700  33.83004052   29.40606209
## 115   30333860    82999 23.108131490 40.456314880  40.45845125   32.66974620
## 117   21148247    26823 56.965397920 42.598615920  29.75532551   29.90046699
## 119   13647793    56066 62.734429070 57.593209340  38.41929141   33.50956822
## 129   18370035    55927 48.653979240 49.518814880  51.53856937   47.14243190
## 130   13072397    36079 36.596885810 36.810121110  17.01702055    7.39119223
## 134   53417691    36981 40.013840830 45.027771610  29.79309986   13.05518246
## 137  281391266    39032 27.161764710 24.794766440  19.51055090   11.18669059
## 139  182830429     2031  0.000000000  0.216479239   0.65008581    0.98950352
## 140   85340849    54366 36.325259520 30.950043250  10.59012936   10.38812009
## 144   21504485    28435 17.936851210 18.384948100  23.58065516   24.38239927
## 148   27187751    10924 58.764705880 51.607050170  45.90796314   38.93462366
## 151  455241296     4232  0.030276817  0.081805683   0.08219550    0.09416226
## 153   36755388    33409 28.989619380 30.424524220  21.34565333   11.21059215
## 154   20575487    23465 40.743079580 35.850129760  22.69715372   13.29916864
## 158    8110911    30313 58.379188710 57.638163620  31.75553660   18.49529343
## 167   18730722    38978 40.617647060 38.991565740  27.19323488   18.95232940
## 172  170749870    11425  0.035467128  1.378027682   1.92242833    1.81347802
## 173  206602384    35055 11.153114190 12.690960210  16.04360884    7.06968069
## 175   68921004    39194  1.713667820  5.880190311   6.61051926    7.77507748
## 177   10721983    16286 59.957612460 57.729238750  28.55478956   18.12438490
## 180    6770280    11510 29.448096890 31.177768170  38.79731620   32.46569834
## 185   32565205    24521 26.134948100 24.370242210  23.13169848   15.96490833
## 193   11328513    15999 38.154844290 29.228157440  26.87878180   20.95286159
## 196   40585058    46145 10.228373700 16.650302770  11.81471189    8.57892309
## 197   15086374    63544 18.666089970 21.315743940  22.83548173   30.13365906
## 200   17970616    19020 50.255190310 40.442041520  22.26135632   21.54934951
## 202  294583151    21427 17.667820070 12.886461940   4.65205816    1.72431558
## 209   24426338    30268 33.910899650 30.267521760  28.59532348   19.65596908
## 213   63184987     9952 19.911764710 29.192906570  20.55866479   14.37787880
## 217   58464478    52252 17.013840830 20.422145330  24.00038390   17.76547799
## 219   43902603    43113  4.467128028  7.536548443  13.73060530   17.59956125
## 220   26345053    31793 58.557093430 52.203703700  29.76887236   23.77365453
## 230   11526212     8638 49.250865050 53.703211010  28.50136484   17.12696099
## 232   25938344    20128 29.800892860 27.150290310  19.73467637   14.57594160
## 233  308580504    18411  0.146384480  0.416884247   0.49060050    1.65611233
## 236   64531856    29290 11.711937720 17.971453290  15.03189631   13.60384630
## 239  106348819    37008  9.601489758 19.177488200  19.26077862   14.95269207
## 240   22687581    39628 23.794117650 21.334126300  19.24932782   15.37007519
## 242 1318545641     6360 11.706747400  8.108131488   2.18799974    0.75048427
## 244 1961914237     6270 17.817474050 19.039497720   3.83393784    1.50247752
## 245  280195894     1417  3.409169550  5.129757785   2.11807940    1.34892641
## 246   29259045    33758 25.121972320 29.919333910  23.63133935    8.49094662
## 247   16927476    36964 27.078719720 34.394679930  27.73157949   11.60978917
## 253   12993375    40959 46.833910030 47.886245670  50.49914999   47.63385206
## 257   12527100    11626 49.870242210 52.538927340  45.83907949   42.79024054
## 261   34163246    42910 31.802768170 28.413062280  29.54526159   26.84758845
## 264   42961291    50955 28.108996540 30.087370240  28.31867908   21.44739863
## 266   12430994     6897  5.591695502  6.378027682   7.25241204    7.43260487
## 268   37767656    26872 18.270761250 22.202205880  14.47040052   15.01401140
## 273  108835425    32704 22.087370240 17.847177600  17.52298883   10.53994784
## 282   48993151     1064  0.947231834  1.251081315   1.09572412    2.35888605
## 283   11681766    19269 56.359861590 49.163607160  32.54386376   21.99368266
## 287  320636133    21009  0.458477509  0.865268166   3.03455003    2.80712640
## 288  320636133    21009  0.088235294  1.780709343   5.99668166    2.30974833
## 290   45976445    33501 34.512975780 28.622621110  27.33282836   17.04582607
## 300    9847717     6726 37.387543250 41.630190310  31.43501187   19.59758001
## 301   16064128    22743 40.532871970 40.122837370  37.21530884   31.60950279
## 304   16488664    19225 51.568339100 39.806444640  19.12024682    7.24924343
## 311    8458861    14609 35.670415220 38.191392730  34.16067270   20.04923779
## 312    8458861    14609 38.437217710 34.165994620  32.50364071   23.07136730
## 314   14655846    16277 39.109861590 37.664576120  25.06006786   12.17476041
## 315    1435639      439 55.486159170 47.223955940  23.08192378   11.92787648
## 316   22768908    19527 40.732495510 25.678315410  18.39363921   12.45801656
## 317   20678502    34107 30.615051900 33.030709340  26.73357354   12.77969663
## 320  242656830    19863 40.174740480 37.206098620  20.06918965   10.25825075
## 322  287014236    28293 26.732698960 27.171280280  12.31863761    4.76933814
## 323   76144562      491  1.311418685  0.600346021   0.46300347    0.76589283
## 325  131951222    13086 20.064013840 20.261910140   7.04379061    3.30263736
## 333    4841212     3785 12.549307960 20.233131490  33.60171759   22.30026336
## 336   24767339    10868 49.388408300 34.868295850  23.09469553   16.95178243
## 337  300828566     2027  1.218858131  1.434472318   0.60403499    0.79411491
## 339  361364714     3583  1.934256055  1.706388763   0.99957645    1.06554288
## 342  272318335     2103  0.145328720  0.415224913   1.40623775    1.10297665
## 351   25001268    18758 19.322751320 25.684882420  13.29137244    8.80782487
## 355  458536402     6844  0.119377163  0.121323529   0.31772375    0.39331821
## 356  124084216    38909 24.178130510 21.174473070  12.16170016    5.76348142
## 359  571041492    49566  8.145328720  8.514057093   7.09401556    4.53095011
## 360  410836962    48194  3.064878893  3.926686851   7.20331270    3.78469670
## 366   18478742    25872 19.910899650 20.168468860  26.53989829   21.61805110
## 368  707062295    55803  3.820069204  6.380269058  10.27862458    4.32489624
## 369  381586639     8205  0.967128028  0.640570934   0.50639018    0.87882803
## 370  520591265    23298  2.179065744  1.340513291   4.49822737    2.69538339
## 373  372865121     6424  0.000000000  1.371107266   2.28199186    1.73192974
## 374   40115011    32384 48.088392860 41.085789710  24.90340853   16.07062570
## 376   66042672    20377  0.000000000  0.036115917   1.96952203    5.12165430
## 377   13156931      701 11.918685120 17.126313490   6.48197912    4.96691059
## 385   20138103    16760 38.389273360 44.414330920  20.51259799   19.69395433
## 386   90633544    20415  4.775951557  4.625114155   3.51360376    4.24781808
## 391   61585318    24355 12.407439450 17.341046710  11.07091506    6.19053821
## 392   38242330    42154 22.786332180 17.268598620  24.88631781   23.83206383
## 393  244939298    44471  6.294117647  4.479661792   1.02248243    2.73573092
## 396    2847143     9313 38.927335640 37.687283740  29.36109178   30.44613618
## 401   17645223    60161 39.589100350 36.682742210  20.15880813   24.94368303
## 406    4811066    16908 60.222318340 56.748269900  23.48564846   15.50719019
## 407   11708211    18203 47.345279720 44.997128340  27.19411279   27.68135136
## 411    1191989     2479 61.506920420 46.594506920  29.92467055   22.03787042
## 412    1191989     2479 43.147923880 43.379757790  29.05872549   21.69613871
## 415    1979040    26125 63.417820070 43.298875430  49.89165083   46.30339141
## 416    3492181    16439 54.667820070 54.516435990  53.99243478   39.89837470
## 422   72168561    27262 29.921480140 37.392100620  24.58664440   10.14453280
## 423   97692930     9310  0.253460208  1.498393021   3.80930716    1.99910069
## 425  391215697    19668  5.705139766  9.669023420  29.32675003   46.74988012
## 435  206211677      549  0.000000000  0.303411953   0.31569003    1.00571965
## 436   69548571     5753  8.287197232  5.802768166   5.29427767    8.81794163
## 437    1559681      953 59.462037040 46.976675720  23.30423924   12.34774037
## 438   13341572    29319 45.504325260 44.075908300  45.52838684   41.58751640
## 443   17501605    32262 56.887543250 50.811202420  60.72008696   65.56690887
## 446   31368242    31173 49.658304500 37.881271630  30.74426438   31.08843930
## 447    8253572     8274 47.708477510 45.179930800  53.38802669   57.32993676
## 451   81814324      324  0.000000000  0.574826990   0.44353509    0.36424634
## 452   43542873    49084 20.817474050 20.019247400  30.37561178   20.99731525
## 453   18071306    35375 25.883217990 28.282223180  36.29082324   30.51484765
## 458  105086001    21968 18.565529620 21.587182970  11.84365321    7.97311154
## 464    8688079     9576 29.085640140 27.634737320  18.63098602   11.50992628
## 467    5349029     3471 33.157439450 18.842560550   8.17597781    5.56893308
## 472  620295438    18403  0.000000000  0.000000000   0.39191975    1.28060367
## 473   20902323    16234 38.859861590 25.674524220  15.59475859   10.96870350
## 477  247178145    18603 13.012500000 14.785762110  15.72400513    6.61577682
## 483  223598466    36280  0.785467128  3.791089965   3.09264073    5.91620997
## 490    6218033    11912 47.232698960 48.236159170  39.40485826   34.91263627
## 492    3864674     2316 61.051038060 49.516652250  38.12130892   33.64095733
## 493    8047826    13774 33.866782010 35.738970590  23.02639318    8.54281570
## 494  363216876    13499  0.168685121  2.277198549   4.57507728    1.89050831
## 496 1170968819    49693 14.752595160 13.761029410  13.41852335    4.41895043
## 503  468659168     2054  0.096020761  0.123702422   0.31675801    0.30982238
## 506 1959419268     3085  0.000000000  0.002811419   1.05585536    0.54777240
## 507    2321651       43  2.211937716  3.246323529   8.08601111    4.89098155
## 509    9746876    23842 31.251730100 32.579152250  39.41728818   33.13224905
## 514  296157543    17999  0.643044619  0.418157720   6.94811058    4.05299326
## 515  343478275    12285  0.000000000  2.143166090   5.41246719    2.05544788
## 516   13863521    46055 54.475778550 52.873053630  52.13239708   45.91377220
## 517  308602532     2340  0.000000000  0.064878893   0.28506136    0.47489812
## 524  111629686    11437 32.492214530 23.395977510   5.34207262    4.86166555
## 525   29002836     7703 27.820909090 26.604461130  12.35462389    6.47581042
## 527  109829121    28626  0.000000000  0.205017301   2.75335850    5.67178188
## 528   27575373    39554 48.930795850 39.782871970  12.27793567   17.83438440
## 532    3249396     2708 37.771626300 27.090181660  36.17731901   40.32269093
## 533    8025452    23851 35.065743940 41.459775090  36.16105000   37.59802474
## 535    3550737    24386 48.269031140 48.479238750  47.86080484   40.00411532
## 536   19159930     4888  1.413494810  1.850562284  15.91524436   19.75612516
## 549  111455506    29840 27.691202870 35.971300450  15.00604088    8.29345748
## 550   26199125    40432 44.192906570 40.922577850  35.66467962   29.02427080
## 553   30049707    12799 25.074141050 27.923976610  42.19711408   46.05492436
## 555   30348270     1343  4.810553633  3.962586505   2.13695415    2.47425751
## 556  143281405     6141  0.101211073  0.181228374   3.34899868    4.63114265
## 558  337668408    46293 36.681660900 31.552119380  14.73705653    5.91020399
## 559  179321360    31013 21.469723180 23.222750870  10.96746173    4.03090315
## 566   12552705    20751 48.054770320 46.248012370  39.11000244   30.10980843
## 568  168962963     1239  0.000000000  0.000000000   0.79306357    0.31162365
## 575    9467889     8793 41.729238750 34.750000000  21.51738115   15.78192728
## 579   35520695    85510 25.558823530 23.576773360  30.81607444   28.94715320
## 581  281410630     5475  0.138408304  0.401234568   1.01791507    1.24879314
## 583    9309984    16597 33.695501730 24.477076120  19.09113594   18.39483336
## 589   59675644    54520 20.457612460 23.438148790  21.41623964   16.98352169
## 603  250829531     2988  0.000000000  0.012110727   0.42921539    0.31913902
## 604   30619956    43931 15.485294120 16.551038060  26.08404476   22.23774382
## 610  156028841    55781 24.707612460 29.713532110  18.69900454    7.77246134
## 611  458186307    52914  4.101211073  7.999773960   5.10204689    4.81433862
## 614  353434267     8686  0.597750865  2.273356401   1.78585794    0.83593435
## 616   64224192    43210  0.663494810  0.649282624   8.47979001   12.04196027
## 617  256402734    33059  0.255190311  3.757791017   5.22096348    1.94604284
## 619 1620564646     1489  0.262110727  0.418181818   0.48255245    0.61910150
## 621   80929583    29850  0.323529412  5.347318339   9.38256972   12.13475045
## 622  677769113     3619  0.000000000  0.075692042   2.03731288    1.33929855
## 625   15590702    12038  3.831314879  3.839033288  14.29326113   12.86259904
## 626   44911607    32999 35.237288140 35.692462090  20.93271964    7.73925779
## 628    9917299    19213 35.653114190 36.757785470  37.81626322   27.71148789
## 630    9917299    19213 35.107843140 39.477611940  40.63998056   28.20096186
## 631    4907885     5586 46.383217990 45.847318340  45.08983299   30.02071038
## 633   22690774    40089 34.087370240 42.450499550  39.11544620   31.10833559
## 636   60393119    45144 42.627162630 45.754974050  34.80759439   34.12072633
## 640    7809213     9570 42.342560550 39.453503460  27.75515496   23.46684271
## 650   32391850    12591  0.086505190  4.021626298  13.12886390   11.04197124
## 652   18251430    28346 30.133752240 29.082013050  29.85237131   21.49011843
## 653   23384827    29290  5.788062284 13.425821800  28.51656230   25.64503635
## 655    1164199     1021 42.779411760 40.377811420  25.80482224   17.26042273
## 657   10877473    11420 55.394463670 54.799091700  35.27212612   26.45648386
## 662    1391166     1053 62.717993080 54.771842560  31.62609810   20.06381224
## 664   25259624    19937 32.160034600 33.519247400  30.62145662   24.04891084
## 669  313459418    17476 12.293252600 16.082761770  12.49803802    6.31374335
## 672   16649433       31  1.304498270  1.859861592   4.08843456    3.50504235
## 674  371190228     5092  0.000000000  0.090614187   0.34412189    0.21483695
## 677 1758347878    58993 15.024221450 15.205017300  11.16425285    6.53944225
## 680  215917460    10528  0.732698962  0.697448097   0.69628607    1.58621435
## 684   25097986    32255 25.408304500 36.415224910  40.00348574   18.91566044
## 686   32304566    36874 52.923875430 36.724697230  24.91394923   16.21288364
## 689   16907018    47596 45.164359860 44.183607270  42.71369619   37.76600805
## 690   33471270    31438 43.634083040 48.153979240  48.74901612   34.56001049
## 691 1271940128    21521  0.007785467  0.049307958   0.52906657    1.82477775
## 692  749321189    16955  0.000000000  0.000000000   1.25694344    1.81434559
## 693  111580289    48349 31.408304500 29.559688580  17.43769784   13.76225710
## 694  105676905     3228  0.626919603  1.004416961   0.90069754    1.15790461
## 695    2607025    10141 54.356401380 52.773572660  39.05039708   28.00063488
## 698   32066841    11588 34.173875430 37.627595160  14.05701516    8.09733698
## 702   43379611    18985 14.649653980 15.076557090  21.89610866   12.38772820
## 703   17658290    21125 25.435121110 28.443339100  23.14566951   19.49087533
## 704   23599705    12513 36.851952770 31.008088070   9.04067306    4.54654969
## 705   62776845    23685 17.109861590 20.479671280  11.04040631    4.62349764
## 709   14821318    35130 42.651384080 38.810121110  21.30373047   16.67137626
## 710   19410241    11382 39.184256060 35.409602080  21.08966165   11.64578668
## 711    6236104     5104 23.437443740 26.943010000  21.67354768   11.89013597
## 714   15621931    41753 38.935121110 32.613754330  27.83334581   16.11738725
## 715   35827006    20447 19.053633220 21.514273360  20.58190920   14.23242042
## 718    3645140    36228 64.583910030 64.628460210  53.60086465   43.87893966
## 720    3273535    13416 64.089965400 53.248839780  51.93263109   42.79014690
## 722  315753777    49331 13.366782010 15.086072660  13.89575202    6.13844673
## 723  237040192     7352  0.000000000  1.049524221   1.44452893    1.55231362
## 725   52958231    39042 33.365051900 31.040224910  24.02216523   13.42528981
## 728   13980575    45199 59.179065740 61.768135900  38.99714373   29.43142924
## 730    6617778     8139 39.049307960 36.256704150  35.28742869   29.46420836
## 734  235303530     5480  0.482698962  0.408307556   1.39586396    1.13004150
## 735  139086997    43220  1.416089965  1.373486159   5.11840378    5.67463024
## 741     485430        0 25.112456750 22.423442910  17.25105757   15.58111183
## 749  712688135      295  0.000000000  0.000000000   0.26997692    0.43943190
## 752  756278009    32980  0.000000000  4.737889273  10.38823143    9.00811799
## 753  183417086    43462  1.942041522  9.246107266  15.92454565    9.77667534
## 756    4434309     5811 43.178200690 43.856185120  26.79740091   17.07131105
## 759  246569347    36298 29.891868510 37.812614260  28.36576935   13.21582337
## 762    3741301     9409 60.365051900 60.769896190  43.07342937   31.05095730
## 765   26391291    30488 22.198961940 19.377595160  15.94506795    9.90912311
## 768   16787888    26036 53.430795850 50.623702420  54.15424540   65.04523327
## 769   16985318    21236 53.450692040 63.633650520  74.59777248   71.37556353
## 770   26147028    27562 37.952422150 37.410899650  28.22177943   31.01069189
## 771   62010184    36489  8.458110517 10.727734810  14.37849526   19.45717385
## 785  498609538    44074 33.029411760 34.046280280  17.88197856    7.31151662
## 797   42184001    26507 20.562283740 17.152622140  19.12264992   10.51072761
## 800   15341366    28185 55.167820070 47.033520760  16.03710092    9.44831705
## 805   51093298    42989 20.584775090 22.556228370  15.43643929   13.42534887
## 807    7243208    27989 12.509515570 10.858996540  21.99952285   24.07428186
## 809   49949933     2565  3.649653979  3.101427336   2.07007112    2.56703557
## 814  234379912    26293 13.983564010  8.523572664   3.57977232    4.97063624
## 815   26832166    17116  9.323529412 12.229671280  12.69131597    5.29865565
## 818    2913325     7031 36.705882350 31.008434260  29.15117968   27.64334564
## 820   52860333    29015 40.211937720 31.171496540  31.41074373   20.29348914
## 830   15187751    14622 26.725778550 32.888408300  12.11484819    5.15565596
## 837    9121644     7112 49.307958480 42.595804500  15.54955983    8.79474982
## 838    1582041     1269  4.194636678  5.360294118   7.88305846    3.48446500
## 843   32418567    12333  3.287197232  8.205666090   6.74325841    6.29888518
## 845   24737298    30611 40.673010380 45.753892730  26.05790814   19.29988369
## 851  190482955    49282 36.752595160 24.439446370   9.58675200    5.02022493
## 855    8503810    42355 58.782871970 52.443987890  38.52252586   32.00897185
## 856   23848404    37701 46.866782010 45.835773820  37.89054231   27.69192056
## 857    1156887      938 62.370242210 60.968641870  40.84958732   30.58771465
## 859   91486480     3330 11.407574390  8.941670349   1.97438356    1.26329962
## 864   32557513    33592 36.352941180 34.586505190  25.08783328   16.01545722
## 870  152691897    35484 55.339965400 48.729671280  23.50255203    8.25109415
## 874 1123566431     5028  0.252595156  0.187716263   0.68594922    0.38343661
##     ImpSrf_15000m CountyArea_m2 CountyPop Log_Dist_PrscRd Log_PriRdLen_5000m
## 3       5.2472094    1534877333     54428        5.760131           8.517193
## 5       5.1612102    1385618994    104430        5.261457           9.066563
## 6       4.7401296    1501737720    101547        7.112373           8.517193
## 7      17.4524844    2878192209    658466        6.600958          11.156977
## 8       4.3006226    2878192209    658466        6.526896          10.915066
## 9       0.1623359    3423328940    194656        9.789557           8.517193
## 14      0.9481135    2878192209    658466        8.734821           8.517193
## 16      7.7170777    3184223082    412992        5.779170          10.364272
## 18     10.9185636    2031190777    229363        7.187640           9.623936
## 20     11.1153413     560435436    189885        5.522936           8.517193
## 24      1.5108669    2049177420     67023        7.041732           8.517193
## 26     42.5553742   15969063883    131346        6.760903           8.517193
## 27      3.2333337   48222689085    134421        6.314788          10.446760
## 28     36.4662683   23828260196   3817117        7.134575          11.187228
## 33      0.1884870   34475546921    200186        9.193844           8.517193
## 37      5.0320363   13896869603    375770        7.845170           8.517193
## 42      0.9595542    1678203880      8715        7.562635           8.517193
## 44      3.6957129    1579271661     50902        5.019187          10.228978
## 46      3.6517172    1755444878     96024        3.289128           8.517193
## 47      0.9000045    1641892684     17997        8.526809           8.517193
## 48      0.7755042    1801758335     21757        7.261019           8.543367
## 50      2.6748149    2104490517     61754        5.096611           9.608993
## 52     13.3991611    1967777404    382748        7.337567          11.421452
## 56      7.1199758    2439681852    203065        6.204129          10.024998
## 62      0.6945969    2641819725     45578        5.623082           8.517193
## 65     23.4995826   15431126407    930450        7.016310          10.296547
## 68     17.6496768    9241044673    134623        6.281180           8.517193
## 69     18.7331710    9241044673    134623        6.370899           8.517193
## 72      4.6401254   10817352524    174528        6.291994           9.460040
## 73      0.2480639   26368354217     18546        6.351006           8.517193
## 78     18.0927628   21061565098    839631        6.568373           8.517193
## 80      0.9530985    3254227528     64665        6.966199           8.517193
## 81     26.0856675   10509869649   9818605        6.041234          10.988538
## 82     30.6315743   10509869649   9818605        6.344698          11.313636
## 89     48.0262563   10509869649   9818605        3.903602          10.539447
## 90      7.8642331   10509869649   9818605        6.867299          10.440055
## 92      4.4558917    5011554741    255793        7.645542           8.517193
## 93      6.6301676    8496702738    415057        7.879342           8.517193
## 94      1.3974245    2480616988     98764        6.717025          10.906160
## 96     48.3694125    2047561084   3010232        7.250344          10.716579
## 99      0.4163350    6612350713     20007        7.962802           8.529855
## 109     2.6584082    3596742302     55269        6.337232           8.517193
## 110    25.2949114   51947229509   2035210        7.680300          10.511916
## 111    10.0724312   51947229509   2035210        6.588919          10.404811
## 114    21.2022833   51947229509   2035210        7.857653          10.500586
## 115    39.7339731   10895120648   3095313        7.744937          11.490633
## 117    31.0346420   10895120648   3095313        5.889929          11.779896
## 119    33.2061175   10895120648   3095313        6.439666          11.573368
## 129    35.4485778    3341343470   1781642        6.801589          11.286887
## 130     7.1697730    1152986019    262382        6.450574          10.237285
## 134     8.4932836    4081430136    483878        5.987186          10.115648
## 137     6.7016981   12494658169    442179        6.656609           9.702769
## 139     0.8185847    4773691889    823318        8.052788           8.517193
## 140    11.7225874    4773691889    823318        6.070393           9.095626
## 144    22.0811319    2067070049    572003        5.201886           9.578615
## 148    33.6251198     396268588    600158        5.811724          11.513138
## 151     0.1490909    4793671177     23086        8.280334           8.517193
## 153     5.9575519    6723613486    299630        6.318517           8.517193
## 154     6.9294753    8622002815    146723       -1.462256           9.677926
## 158    11.9566578    1618456437    916829        2.886065          10.867445
## 167    12.6638734    1565663096    862477        6.716950          11.349773
## 172     2.2404895    1518196116    162310        6.357293           8.517193
## 173     3.9705766    1518196116    162310        2.214658           8.530172
## 175     8.1856657    1104074798    538479        6.529542           8.517193
## 177    13.0534610    1104074798    538479        4.560810          11.361322
## 180    26.1544088     158114680    601723        5.939102          11.448810
## 185    13.9570750    2630557912    543376        6.862799           9.280769
## 193    17.8455963    2642341101   1229226        4.791074          10.696502
## 196     5.6703336    1727138746    275487        5.098285          10.334628
## 197    25.8214977    4915061046   2496435        6.369778          10.764004
## 200    22.7603321    2339870128   1145956        4.538834           9.726365
## 202     1.0193743    5101663125   1320134        7.674137           8.517193
## 209    21.4043266    1439690708    379448        7.700367           9.497963
## 213     9.8684097    1104465640    265128        6.238530          11.621291
## 217    15.5336897     879428364    688078        7.202209          11.443959
## 219    21.1543939     693033963    691893        6.932028          11.348749
## 220    21.5227386     693033963    691893        4.563606          11.375301
## 230    10.9352231     560435436    189885        6.267272          10.228193
## 232    10.5070682     560435436    189885        7.030366          10.758131
## 233     1.3624822     803754838     41475        8.638483           8.517193
## 236    10.5055549    1156117093     68756        6.632640           9.374314
## 239    10.1356848    2726158067    392365        6.829740          10.837257
## 240     9.6645057    2726158067    392365        5.425693           9.559563
## 242     0.4608820    2011429331      9285        5.213907           8.517193
## 244     0.7811719   11819118494      7936        5.851135           8.517193
## 245     0.8126662    6810799882     12765        7.611572          10.608780
## 246     4.7797337    2214963578     67103        6.690377           9.751087
## 247     6.4100834    2580316235    201081        6.537995          10.333022
## 253    43.2251298    2448383588   5194675        6.627345           8.538217
## 257    41.1653946    2448383588   5194675        6.029633           9.786552
## 261    27.8268133     848218379    916924        7.789542           9.334756
## 264    17.4038568    1346943286    515269        6.624206          10.041881
## 266     9.0950386    1149099822    703462        7.469536           8.517193
## 268    14.3815032    1562206475    308760        7.244290           8.533759
## 273     6.9998911    1853347576    269282        4.826338           8.721351
## 282     2.3677934    1752271023    113449        6.023027           8.517193
## 283    12.3990013    1329601795    295266        4.223333           8.662116
## 287     1.6052756    1106622334     41889        7.706197           8.517193
## 288     1.5762059    1106622334     41889        7.699416           8.517193
## 290    10.8393664    1199605640    197559        6.514821           9.047706
## 300    20.4009781    1292303671    496005        6.435126          10.951465
## 301    27.6881849    1292303671    496005        4.976504          10.908938
## 304     4.2766561    1170454727    131636        6.048040           8.517193
## 311    13.1383248    1185826798    266931        5.059614          10.305430
## 312    13.7884643    1185826798    266931        6.709637          10.878554
## 314     6.0514130    1294491529    172780        5.641494           9.888527
## 315     7.2238476     604697995    179703        6.334829           9.363844
## 316     6.8800866     604697995    179703        7.317122           8.517193
## 317     7.6343847     604697995    179703        5.680478           9.763274
## 320     6.2011954    1465333940    131090        5.191200           9.400834
## 322     2.7482083    1799821282     49116        6.597922           8.517193
## 323     0.9325887    1496381153     17764        8.575773           8.517193
## 325     2.2959440    1340366450     35862        4.874397           8.517193
## 333    17.0784755    2461213949     93158        5.789315          10.837193
## 336    12.8303747    1186444226    165224        6.148184          10.172046
## 337     0.6457308    1255597645      7570        5.925072           8.517193
## 339     0.8429762    1503286817     13229        4.827232           8.517193
## 342     0.7338603    1538604962      9656        6.720172           8.517193
## 351     6.9316705     414046208     49542        6.779779           8.517193
## 355     0.5649423     969940558     12460        5.926369           8.517193
## 356     2.9858240    1187111257     96656        4.386866           8.803877
## 359     2.4779218     538061269     49285        7.363009           8.517193
## 360     2.2686828    1614282063    105543        6.553245          10.750597
## 366    18.8490590     415044980    159720        2.068241          11.143917
## 368     2.8225914    1132583005     82916        5.530689          10.133252
## 369     0.8348565    1521032417     23842        7.571922          10.085873
## 370     2.1134106    2037887589     65024        5.206763           8.517193
## 373     1.3900614    2754864273    192768        6.604687           9.957431
## 374    11.1352129    2754864273    192768        5.179874          10.849479
## 376     6.5071486    1179412087    440171        7.928563           8.517193
## 377     5.8065642    1602236448     33387        3.680138           8.517193
## 385    18.3268725     977764266     35897        5.175603           8.517193
## 386     3.2868471    2049391733    121097        5.141601           9.331428
## 391     7.1514304    1549594703    805029        6.640054          10.307858
## 392    19.8086392    1549594703    805029        5.449489          11.151308
## 393     5.2072349     896842957    101108        4.736126           8.517193
## 396    24.2990266    1250163582    863420        3.621094          10.868872
## 401    20.9250383     209643241    620961        4.896128          10.610362
## 406    10.1507458    1432510950    548285        5.779904          10.575000
## 407    24.2175840    1275732137    743159        6.634540           8.517193
## 411    16.0214142    1598385896    463490        6.110227          10.909299
## 412    16.0650640    1598385896    463490        4.095634          10.874658
## 415    33.7395510     150618894    722023        4.052612          11.628408
## 416    32.4947065     150618894    722023        4.133293          11.620994
## 422     6.9206539    1145557748    107771        5.943211          10.565608
## 423     2.1805585    1470457874    156813        7.970059          10.558056
## 425    49.0478254    4036289692     38520        4.673200           9.998064
## 435     0.8847985    1462634072     14849        6.732059           8.517193
## 436    10.8535405    1422924260    152021        4.466086          10.687363
## 437     7.1178740    1293040828    172188        2.338427           9.888806
## 438    42.3871151    2247237402   1202362        7.343914          10.077511
## 443    66.1560786    1585280173   1820584        3.510144          11.366125
## 446    28.4267861    1585280173   1820584        4.567776          10.732978
## 447    61.2271585    1585280173   1820584        7.543749          11.316717
## 451     0.2705767    5235770376     28567        9.474679           8.517193
## 452    19.2670326    1456007312    398552        6.745190          10.538180
## 453    31.1318223    1433793826   1152425        7.221479          10.762975
## 458     5.1352471    1692165422    144248        3.282982           8.517193
## 464     6.8143105   16180692391    200226        4.932965          10.579533
## 467     4.5603860     995285532    238136        6.233762           8.517193
## 472     1.2241451    1093251406     21906        8.239864           8.517193
## 473     7.4764868    1486637454    187105        7.277701           8.517193
## 477     3.4363088    1822402881     80261        7.256593          11.065319
## 483     4.9243190    1028998027    221939        6.346836           9.958925
## 490    27.7034412     160343174    319294        5.792187          11.549682
## 492    27.0335476     160343174    319294        5.882251          11.523917
## 493     4.2360897    6988196577     81327        6.234598          11.493261
## 494     1.7277821   13176979222     90928        7.007866           8.517193
## 496     2.6308519   13176979222     90928        6.977756           8.517193
## 503     0.1992169    6716936093    109299        7.416969           8.517193
## 506     0.3147926    7149723773     11413        8.176879           8.517193
## 507     2.5540739    1860847940     34200        8.231527           9.891906
## 509    24.5115349     850693384    517110        7.308713          10.944594
## 514     2.3013205    1915039277     36970        7.923347           8.517193
## 515     1.3912386    1009986004     20234        7.003711           8.517193
## 516    37.1244420   20438710673   1951269        6.568149          11.624229
## 517     0.3665037   20438710673   1951269        8.116774           9.609929
## 524     5.9903979    2419349805    146445        5.707519          10.458903
## 525     6.4510628    2565935077    197131        6.597414          10.636316
## 527     6.4208385    1439267859    274549        7.396768           8.517193
## 528    31.3378703    1439267859    274549        5.380933           8.537774
## 532    39.9056636     603490137    905116        7.129030          10.648950
## 533    34.2897117     573067842    513657        5.647454          11.430740
## 535    33.4017446     326888224    783969        6.802030          10.292121
## 536    20.8496994     833989655    288288        7.354081          10.831652
## 549     5.8453931     924412063    108692        6.458374          10.268131
## 550    18.7818373    3006530549    662564        6.740597          11.289973
## 553    50.1760883    9861408558    209233        6.319924          11.290904
## 555     1.5165570   10260561575     29514        5.479758           8.517193
## 556     2.5977102   11372460346     64727        8.025371           8.517193
## 558     3.2649140   14278776370    130044        6.319245           8.517193
## 559     2.1811098    4945359181    144170        3.955202          10.208422
## 566    31.4682807    2700563452    919040        2.033161          10.698671
## 568     0.2952681    4647029522     39370        7.527404           8.517193
## 575    11.1193452    2016019983    467026        6.045674          10.584822
## 579    30.1856124     151178512    468730        7.115295          10.713175
## 581     1.2347673    3601531651     98990        6.766147           8.517193
## 583    18.1393361    1114982482    949113        4.888892          11.368267
## 589    11.2669557    1689487711    319431        6.396219           8.517193
## 603     0.7951191    1194547357     24505        7.330811           8.517193
## 604    19.3984931    1356745512    919628        7.895353           9.649576
## 610     4.0005421    1688606138    168148        6.003402           8.517193
## 611     3.7024405    1688606138    168148        6.421012           8.517193
## 614     0.6278083    1367504099     13981        6.540096           8.517193
## 616    11.1067230    2163206258    900993        7.765304          10.910740
## 617     1.1147087     809515805     51079        6.679800           8.517193
## 619     0.5222704    2975515808       783        7.998508           9.908590
## 621     8.9737945    4571166077    149778        6.343578          10.712244
## 622     0.8102143    2701246664      8424        8.528949           8.517193
## 625    11.4947054    1209668470    368130        5.573650           8.517193
## 626     4.2150080    1029450254    138333        5.717090           9.685788
## 628    22.5139117    1184118946   1280122        4.358720          10.993587
## 630    23.6167378    1184118946   1280122        4.545377          10.932851
## 631    24.7167389    1184118946   1280122        4.193005          10.667788
## 633    25.0819147    1184118946   1280122        5.605433          10.815928
## 636    28.1989591    1378361040   1163414        5.803574          11.309341
## 640    22.1925327    1051302780    802374        3.761575           9.865007
## 650     9.4258476    1271946706    301356        7.150964          10.139685
## 652    16.0404544     882810658    441815        7.399141          10.262591
## 653    20.1662478     882810658    441815        6.528500          10.848474
## 655    11.9461181    1066098928    238823        5.207158          10.641838
## 657    19.8395391    1195417263    535153        5.062413           9.925069
## 662    13.0778375    1489943930    375586        4.508541          10.474530
## 664    16.7195140    1069012672    541781        5.397366          10.691963
## 669     3.3205987    2099056912     70990        5.823957           8.517193
## 672     2.2828962    1219421293     31848        6.023053           8.517193
## 674     0.6252810    1743764515     42391        7.559153           8.517193
## 677     3.5945574    7817065156    157733        7.700556           8.517193
## 680     2.2387589    7209356169    203206        7.081952           8.517193
## 684    10.8042325   11792524334    351715        7.072527           9.516444
## 686    11.0243489   11792524334    351715        3.018341          11.047425
## 689    32.1846828    1117054236    735334        6.955998          10.865651
## 690    33.5792844    1117054236    735334        6.480461          11.353199
## 691     1.1149661    8328130471     75889        8.364663           8.517193
## 692     1.0565744    5274784008     25748        8.406553          10.308810
## 693    10.8916348    1875746999    529710        7.633282           9.797037
## 694     1.5639484    1343342705    101407        6.651112           8.517193
## 695    24.3285715    1890884266   1223348        6.281415          11.352714
## 698     6.8466145    1890884266   1223348        6.385141           8.517193
## 702     7.9386019    2218341544    411442        6.821359           9.131517
## 703    18.5056999    1565148677    625249        2.527939          11.182035
## 704     2.5280683    1782819861    143679        6.605884           8.517193
## 705     2.8301026    2874682925    153990        6.093232           8.556108
## 709    15.2377814     476152313    558979       -0.167176          10.615420
## 710     6.8671794    2069799485    280566        5.151823           8.517193
## 711     7.0492390    1189006298    214437        6.906396          10.427861
## 714    15.0272907    1251067046    799874        6.657300          11.574515
## 715    12.7636067     957444154    297735        8.077430           9.789158
## 718    34.3071819     347321129   1526006        0.244920          11.872358
## 720    34.6113784     347321129   1526006        4.687935          11.640534
## 722     3.8878286    2219591093    207820        4.915074          10.269291
## 723     2.4607657    2219591093    207820        6.600319           8.708258
## 725     8.1922143    2341819225    434972        5.987619          10.362150
## 728    22.1386381    1060604571    626667        4.847115          10.852575
## 730    23.2928852    1060604571    626667        6.252943          10.989115
## 734     0.8158585    1296046259     26985        7.537304           8.517193
## 735     4.1582521    2071897847    136885        7.576233           9.532329
## 741    12.9793081    1960797690    384504        5.744930          10.101940
## 749     0.4193461    4827514117      3031        7.209915           8.517193
## 752     5.3391622    7191239757    100948        6.673186          10.826625
## 753     5.2631775    7191239757    100948        6.555430           8.600202
## 756    12.1054110    1404890184    336463        5.431576          10.443126
## 759     7.1990980    2292153748     92565        6.109818          10.409153
## 762    29.2631330    2256602704   2368139        5.425112          12.013498
## 765     5.4005623    2324999033    137130        6.060328          10.139866
## 768    60.5900483    2622862905    800647        4.368874          11.099817
## 769    68.5181921    2622862905    800647        3.968919          11.148788
## 770    30.7030179    4411986582   4092459        7.008461           8.517193
## 771    19.2594764    4411986582   4092459        7.134172          10.645648
## 785     4.3352668    3016851000    112656        5.390011           8.517193
## 797     8.0839814    1492050864    231236        3.827340          10.478768
## 800     5.0652291    1389731195    156545        5.755803          10.831303
## 805    12.5720262    1096334108    316236        4.942640          10.667855
## 807    21.2887388    1012604465   1081726        5.187663          10.515353
## 809     3.3632614    1070949703     78305        5.621719          10.012115
## 814     3.7874110    2199121564     76314        4.996663          10.132054
## 815     3.2261085      33703512     17835        7.123645          10.952743
## 818    20.4729928     140171293    242803        4.034064          10.757877
## 820    11.2394281     110234185     97032        4.681545          10.733698
## 830     3.4414421     831754462    104169        1.645892           9.595364
## 837     6.0661987    2335100448    193063        5.373161          10.235822
## 838     2.1121107     799620921     56418        5.997960           9.530316
## 843     5.2323572     948607826     86956        6.119572           8.517193
## 845    11.6350822    1371938244    248007        5.421107          10.174230
## 851     4.2529938    1169862598    114638        5.535058           8.517193
## 855    23.7479441     625228895    947735        5.332814          11.217841
## 856    22.2725708     625228895    947735        6.196465          11.126329
## 857    24.2936125     625228895    947735        5.755181          11.224327
## 859     1.7568425     603666538     86395        5.058056          10.728035
## 864    14.5017723    1423388982    389891        4.394461          10.271998
## 870     4.0382790    6956479515     91738        6.023511          11.014742
## 874     0.2601246   12656072085     10247        7.927885           8.517193
##     Log_PriRdLen_10000m Log_PriRdLen_15000m Log_PriRdLen_25000m
## 3              9.274303            9.658899            10.15769
## 5             11.137360           11.587258            12.01356
## 6              9.210340            9.615805            10.12663
## 7             11.849658           12.401245            12.98762
## 8             11.728685           12.230208            12.86472
## 9              9.210340            9.615805            10.12663
## 14            10.205823           11.380790            11.85793
## 16            11.116022           11.706608            12.23758
## 18            11.134147           11.608096            12.12632
## 20            11.363701           11.657322            12.05099
## 24             9.210340            9.615805            10.12663
## 26             9.210340            9.615805            10.12663
## 27            11.322142           11.986295            12.59834
## 28            12.041584           12.487677            12.95395
## 33             9.210340            9.615805            10.12663
## 37             9.246966            9.640371            10.14144
## 42             9.210340            9.615805            10.12663
## 44            11.043768           11.538634            12.42227
## 46             9.267750            9.693229            11.10778
## 47            10.609678           11.097203            11.67865
## 48             9.223513            9.624606            10.15902
## 50            10.352943           10.765148            11.40833
## 52            12.437953           12.938158            13.36950
## 56            11.816822           12.183208            12.48763
## 62             9.210340            9.615805            10.15508
## 65            11.196586           11.484608            11.79973
## 68             9.210340            9.615805            10.12663
## 69             9.210340            9.615805            10.12663
## 72            10.272648           10.699374            11.30947
## 73             9.210340            9.615805            10.18209
## 78             9.211135            9.616335            11.43024
## 80             9.210340            9.615805            10.56825
## 81            12.141433           12.631789            13.31298
## 82            12.766742           13.311711            14.13706
## 89            11.854460           12.799036            13.68739
## 90            11.185359           11.505800            12.07592
## 92             9.210340            9.615805            10.13391
## 93             9.210340            9.615805            10.22256
## 94            11.091275           11.250175            11.77927
## 96            11.422561           12.444049            13.41317
## 99             9.216691            9.620044            10.67846
## 109            9.210340           10.506685            11.17724
## 110           11.700147           12.291710            12.98691
## 111           11.052332           11.441351            12.11731
## 114           11.641090           12.093382            12.94328
## 115           12.399015           12.910645            13.52133
## 117           12.846330           13.491999            13.88062
## 119           12.797699           13.251158            13.79533
## 129           12.326560           12.808731            13.17874
## 130           10.970173           11.263167            11.66891
## 134           10.825729           11.284782            11.90145
## 137           10.670001           11.302436            11.64735
## 139            9.210340            9.615805            12.06101
## 140           10.438968           11.805347            13.34354
## 144           10.812050           12.437657            13.28737
## 148           12.552370           12.990455            13.66067
## 151            9.210340            9.615805            12.46996
## 153           11.072707           11.691640            12.27618
## 154           11.263470           11.735927            12.37850
## 158           12.070255           12.515037            12.95021
## 167           12.019183           12.425254            13.05034
## 172            9.210340            9.615805            10.13448
## 173            9.216851            9.620151            10.12924
## 175           10.677785           11.508043            12.50463
## 177           12.157118           12.432969            12.85808
## 180           12.409525           12.958102            13.76492
## 185           10.309049           10.742060            11.37495
## 193           11.597292           12.016302            13.04943
## 196           11.120939           11.521223            12.08251
## 197           11.322010           11.717280            12.79773
## 200           10.961388           11.740006            12.73101
## 202            9.210340            9.615805            10.12663
## 209           10.903851           11.513795            12.24009
## 213           12.034500           12.377475            12.84753
## 217           12.066111           12.400894            13.07402
## 219           12.275288           13.205841            13.84881
## 220           12.132928           12.528570            13.61554
## 230           11.396026           11.694368            12.08202
## 232           11.261575           11.543111            11.95726
## 233            9.210340            9.615805            10.61557
## 236           11.232785           11.884424            12.66412
## 239           11.642560           12.093105            12.71227
## 240           11.292305           11.964427            12.64087
## 242            9.210340            9.615805            10.12663
## 244            9.210340            9.615805            10.12663
## 245           11.339410           11.710576            12.21412
## 246           10.761122           11.097103            11.54471
## 247           11.547405           11.986278            12.50362
## 253           11.427997           12.194246            13.11483
## 257           11.047782           11.938442            13.15084
## 261           10.883949           11.810373            12.62948
## 264           10.671999           11.107670            12.07335
## 266            9.212138           11.490604            12.29050
## 268            9.250029            9.642439            11.70844
## 273            9.317621            9.688589            11.85080
## 282           10.395377           11.104044            11.68757
## 283           11.092882           11.828117            12.49342
## 287            9.210340            9.615805            11.52577
## 288            9.210340            9.615805            10.95215
## 290           11.571122           12.221943            12.87292
## 300           11.724020           12.143894            12.76039
## 301           11.760029           12.251795            12.93350
## 304           11.454928           11.676556            12.05415
## 311           12.046281           12.621617            13.02347
## 312           12.148892           12.688977            13.05605
## 314           10.779736           11.209038            11.64144
## 315           10.575723           11.092540            12.00841
## 316           10.412932           11.226282            12.04149
## 317           10.869420           11.143294            12.01866
## 320           10.759259           11.163602            11.53158
## 322            9.210340            9.615805            12.02065
## 323            9.210340            9.615805            10.73998
## 325            9.210340            9.615805            10.12663
## 333           11.995105           12.581973            13.14398
## 336           11.391961           12.131141            12.63965
## 337            9.210340            9.615805            10.12663
## 339            9.210340           10.468232            11.43152
## 342            9.210340            9.615805            10.12663
## 351           10.150854           11.061244            11.72126
## 355            9.210340            9.615805            10.12663
## 356           10.424235           11.140943            11.82204
## 359           10.571323           11.115314            11.84480
## 360           11.454810           11.855892            12.34785
## 366           12.055525           12.448545            12.98373
## 368           10.827304           11.263362            11.82508
## 369           11.280882           11.990761            12.85894
## 370            9.210340            9.615805            10.12663
## 373           10.766999           11.194631            11.88625
## 374           11.576119           11.793016            12.13647
## 376            9.500309           10.807520            11.61099
## 377           10.136412           11.005550            11.74554
## 385           10.900331           11.836608            12.22581
## 386           10.256561           11.385934            12.05991
## 391           11.509571           12.089549            13.15763
## 392           12.222729           12.744955            13.58204
## 393           11.078797           11.704318            12.39066
## 396           12.441358           13.100395            13.72929
## 401           12.086384           13.060478            13.71012
## 406           11.361398           11.718646            12.38569
## 407           10.755527           12.132764            13.15280
## 411           12.070491           12.420370            12.90297
## 412           12.057138           12.411431            12.90038
## 415           12.284280           13.006444            13.66248
## 416           12.163419           12.512073            13.64783
## 422           11.535059           12.053943            12.60304
## 423           11.729217           12.161154            12.58800
## 425           10.517277           10.857828            11.33351
## 435            9.210340            9.615805            11.05070
## 436           11.332178           11.892980            12.75759
## 437           10.930895           11.408769            11.88747
## 438           11.749469           12.641576            13.57649
## 443           12.348770           12.792937            13.38908
## 446           11.784169           12.182629            13.08026
## 447           12.426446           12.839899            13.47436
## 451            9.210340            9.615805            10.12663
## 452           11.231269           11.981318            12.95254
## 453           11.727568           12.588594            13.41797
## 458           10.519504           11.077042            11.66377
## 464           11.039108           11.255082            11.50839
## 467           10.730253           11.476555            12.52940
## 472           10.165964           11.229363            11.76538
## 473           10.666481           11.373478            11.90933
## 477           11.638982           11.944382            12.37128
## 483           11.023920           11.959875            12.80838
## 490           12.287657           13.067936            13.75681
## 492           12.287250           13.069321            13.75567
## 493           12.208436           12.483380            12.89152
## 494            9.210340            9.615805            10.12663
## 496            9.210340            9.615805            10.12663
## 503            9.210340            9.615805            10.12663
## 506            9.210340            9.615805            10.12663
## 507           11.576213           11.973141            12.62754
## 509           11.950032           12.697286            13.09864
## 514            9.210340            9.615805            10.30027
## 515            9.210340           11.187835            12.30055
## 516           12.417507           12.969315            13.52672
## 517           10.705289           11.164123            11.80332
## 524           11.447336           12.316280            12.92260
## 525           11.515213           12.044336            12.63783
## 527            9.210340            9.622713            10.17055
## 528            9.220684            9.622713            10.17055
## 532           11.781419           12.594654            13.65254
## 533           12.482345           12.887383            13.47823
## 535           11.761297           12.393022            13.32740
## 536           11.942171           12.643546            13.46986
## 549           11.056371           11.406268            11.86995
## 550           12.118298           12.505068            13.05595
## 553           12.044936           12.398740            12.82375
## 555            9.210340            9.615805            10.12663
## 556            9.210340            9.615805            10.12663
## 558            9.252573            9.670061            10.23859
## 559           11.375976           11.927421            12.66838
## 566           11.851505           12.311486            12.87774
## 568            9.210340            9.615805            10.12663
## 575           12.111553           12.512126            12.96163
## 579           11.776145           12.393307            13.19763
## 581           11.305164           12.276983            12.86996
## 583           12.598658           13.226603            13.88979
## 589           10.741996           11.821364            12.35355
## 603            9.210340            9.646777            10.14533
## 604           11.793185           12.581573            13.40365
## 610            9.210340            9.615805            10.12989
## 611            9.210340            9.615805            10.12989
## 614            9.210340            9.615805            10.12980
## 616           11.918997           12.426475            12.88330
## 617            9.210340            9.632637            10.23905
## 619           11.021073           11.502965            12.05331
## 621           11.655740           12.125090            12.63919
## 622            9.210340            9.615805            10.12663
## 625            9.842891           10.783059            12.42644
## 626           10.852901           11.326243            11.98754
## 628           11.985496           12.429279            13.37594
## 630           12.016720           12.429171            13.37649
## 631           12.024774           12.616430            13.38223
## 633           11.978597           12.656250            13.47358
## 636           12.642039           13.161784            13.61298
## 640           11.311574           12.159000            13.00342
## 650           11.584185           12.316694            12.88201
## 652           11.464039           12.402120            13.17270
## 653           12.354734           12.722396            13.16415
## 655           11.731803           12.469426            13.13328
## 657           10.899391           11.695319            12.34466
## 662           11.018451           11.377836            11.77874
## 664           11.804338           12.310307            13.17999
## 669           11.021256           11.344803            11.72831
## 672           10.607691           11.119978            11.69044
## 674            9.210340           10.414421            11.57796
## 677            9.210340            9.615805            10.12663
## 680            9.210340           10.871421            11.85357
## 684           11.194140           11.622989            12.08762
## 686           11.516061           11.777533            12.16175
## 689           12.548681           13.121125            13.53814
## 690           12.438884           13.040450            13.52361
## 691           10.857355           11.489329            12.33231
## 692           11.821355           12.308295            12.76296
## 693           10.968626           11.358781            12.52438
## 694            9.210340            9.615805            11.47320
## 695           12.221658           12.875175            13.49012
## 698            9.210340           11.307367            12.47596
## 702            9.765258           10.468650            12.25520
## 703           12.150971           12.702763            13.27617
## 704            9.812215           10.146395            10.47726
## 705            9.229987            9.634950            11.76042
## 709           11.857942           12.533980            13.54580
## 710           10.860349           11.497962            12.25638
## 711           11.873269           12.284037            12.71930
## 714           12.520181           12.891484            13.51160
## 715           10.836990           11.415239            12.49414
## 718           12.535338           12.919327            13.72243
## 720           12.468940           12.899789            13.79158
## 722           10.963037           11.401467            12.20775
## 723            9.359044            9.717356            11.85485
## 725           10.771717           11.051243            11.53006
## 728           12.178103           12.745765            13.26996
## 730           12.093354           12.705687            13.23851
## 734            9.210340            9.615805            11.60374
## 735           10.751894           11.136604            11.70463
## 741           10.924146           11.470145            12.52285
## 749           10.435528           11.044472            11.68015
## 752           11.623030           12.041045            12.54846
## 753           11.005037           11.681622            12.37392
## 756           11.053602           11.615405            12.62244
## 759           10.911749           11.226903            11.66023
## 762           12.646347           13.103172            13.89057
## 765           10.916242           11.410619            12.00912
## 768           11.871891           12.289860            12.81947
## 769           11.879212           12.285470            12.79035
## 770           11.443001           12.638809            13.57742
## 771           11.414800           11.862607            12.86719
## 785            9.210340            9.616890            11.15956
## 797           11.406619           11.837234            12.43098
## 800           11.510515           11.896597            12.66703
## 805           11.726471           12.433155            13.16133
## 807           12.487088           13.101585            13.55403
## 809           10.692505           11.071809            11.56201
## 814           10.838870           11.245473            11.86624
## 815           11.477252           11.767294            12.16223
## 818           11.812035           12.592103            13.03949
## 820           11.925001           12.516983            12.92051
## 830           10.341123           10.741298            12.32899
## 837           11.733183           12.389761            12.88941
## 838           10.762602           11.172123            11.94087
## 843           10.820432           11.517647            12.11044
## 845           10.852852           11.114485            11.48581
## 851            9.210340           10.736408            11.65673
## 855           12.037502           12.504575            12.96672
## 856           12.107686           12.513956            12.92005
## 857           11.996550           12.525460            12.98440
## 859           11.389017           11.701285            12.25433
## 864           11.212421           12.175898            13.14080
## 870           11.906102           12.324131            12.78463
## 874            9.210340            9.615805            10.12663
##     Log_PrscRdLen_500m Log_PrscRdLen_1000m Log_PrscRdLen_5000m
## 3             8.611945            9.735569           11.770407
## 5             8.740680            9.627898           11.728889
## 6             6.214608            7.600902           12.298627
## 7             6.214608            9.075921           12.281645
## 8             6.214608            8.949239           11.039001
## 9             6.214608            7.600902            8.517193
## 14            6.214608            7.600902            8.517193
## 16            7.595229            8.658654           11.748979
## 18            6.214608            7.600902           11.473810
## 20            8.320842            9.324509           12.265658
## 24            6.214608            7.600902           11.263953
## 26            6.214608            8.196272           10.578712
## 27            6.214608            9.563727           11.642077
## 28            6.214608            7.600902           11.524040
## 33            6.214608            7.600902            8.517193
## 37            6.214608            7.600902           10.525636
## 42            6.214608            7.600902           10.420835
## 44            7.274460            8.810625           10.731814
## 46            7.823183            8.708900           11.002084
## 47            6.214608            7.600902            8.517193
## 48            6.214608            7.600902           10.450983
## 50            7.775346            8.689372           10.978451
## 52            6.214608            7.600902           12.062040
## 56            6.214608            8.928575           11.407706
## 62            7.617172            8.708766           10.116661
## 65            6.214608            7.600902           10.737947
## 68            6.214608            9.352865           11.226185
## 69            6.214608            9.327359           11.175748
## 72            6.214608            8.551344           10.430496
## 73            6.214608            8.195890            9.617658
## 78            6.214608            8.477044           10.959837
## 80            6.214608            7.600902           10.512377
## 81            7.670002            9.256363           11.441191
## 82            6.214608            9.262183           11.492556
## 89            7.816724            8.696727           11.258118
## 90            6.214608            7.852470           11.108810
## 92            6.214608            7.600902           11.130320
## 93            6.214608            7.600902           11.016846
## 94            6.214608            9.053811           11.302746
## 96            6.214608            7.600902           11.332527
## 99            6.214608            7.600902           10.179840
## 109           6.214608            8.698558           11.236743
## 110           6.214608            7.600902           10.874393
## 111           6.214608            8.543798           10.884304
## 114           6.214608            7.600902           10.670897
## 115           6.214608            7.600902           11.654502
## 117           7.925588            9.681314           11.866923
## 119           6.214608            8.828726           11.717448
## 129           6.214608            7.993257           11.575105
## 130           6.214608            8.555506           10.690128
## 134           8.160745            9.251122           10.867117
## 137           6.214608            8.662137           11.000477
## 139           6.214608            7.600902           10.545898
## 140           7.663066            9.161012           10.818938
## 144           7.796059            8.701215           10.844964
## 148           8.178463            9.590114           12.118715
## 151           6.214608            7.600902            9.151503
## 153           6.214608            8.783157           10.758653
## 154           8.136272            9.300562           11.276146
## 158           8.853998            9.899072           11.843622
## 167           6.214608            9.037500           12.154056
## 172           6.214608            9.198363           11.341830
## 173           7.820293            9.422886           12.316827
## 175           6.214608            9.226355           11.826570
## 177           9.182474           10.471049           12.690103
## 180           8.148503            9.552943           12.070162
## 185           6.214608            8.088255           11.387856
## 193           8.491501            9.302532           11.984032
## 196           8.111997            9.327349           11.757618
## 197           6.214608            8.607165           11.646377
## 200           7.807065            8.693256           12.014368
## 202           6.214608            7.600902           10.959465
## 209           6.214608            7.600902           11.172902
## 213           6.214608            9.988227           12.242222
## 217           6.214608            7.600902           12.028914
## 219           6.214608            7.600902           11.511094
## 220           8.643868            9.630551           11.912788
## 230           6.214608            9.582491           12.420900
## 232           6.214608            7.600902           11.998750
## 233           6.214608            7.600902            8.517193
## 236           6.214608            7.826166           11.756870
## 239           6.214608            8.621097           11.090403
## 240           8.068897            9.046820           10.962943
## 242           7.849256            8.882426           10.668350
## 244           7.434724            8.604901           10.604485
## 245           6.214608            7.600902           10.608780
## 246           6.214608            8.367262           11.624364
## 247           6.214608            8.473831           11.579432
## 253           6.214608            7.652655           10.951940
## 257           7.824192            9.299264           11.171908
## 261           6.214608            7.600902           10.556261
## 264           6.214608            8.667757           11.452380
## 266           6.214608            7.600902           10.352121
## 268           6.214608            7.600902           10.876699
## 273           8.126889            9.233145           11.595505
## 282           7.375690            8.418383           10.596130
## 283           8.820987            9.593653           11.385535
## 287           6.214608            7.600902           10.125906
## 288           6.214608            7.600902           11.001669
## 290           6.214608            8.048253           11.470999
## 300           6.214608            8.873185           11.611654
## 301           7.789508            8.690555           11.552441
## 304           7.323708            8.624370           11.636138
## 311           8.131450            8.958110           11.376859
## 312           6.214608            8.415227           11.577732
## 314           8.224503            9.378968           11.897445
## 315           6.214608            9.030428           11.752648
## 316           6.214608            7.600902           11.586764
## 317           8.247282            9.680957           11.689477
## 320           7.986986            8.920757           10.893800
## 322           6.214608            8.591997           11.286961
## 323           6.214608            7.600902            8.517193
## 325           8.122912            8.985838           10.949190
## 333           7.576519            8.642548           11.469740
## 336           7.017561            8.636803           11.642114
## 337           7.491485            8.643617           10.218471
## 339           7.289407            8.287900           10.364311
## 342           6.214608            8.333096           10.742540
## 351           6.214608            8.307334           11.661978
## 355           7.484374            8.675520           11.206761
## 356           8.530520            9.282196           11.662360
## 359           6.214608            7.600902           11.535209
## 360           6.214608            8.916350           12.085583
## 366           8.462708            9.944601           12.478702
## 368           7.783940            9.074932           11.682053
## 369           6.214608            7.600902           10.659500
## 370           7.762536            8.709596           11.691687
## 373           6.214608            8.115973           10.661254
## 374           8.114764            9.350786           11.753441
## 376           6.214608            7.600902           10.184258
## 377           8.011141            8.854809           11.119268
## 385           8.771385           10.024988           11.961131
## 386           7.850262            8.815132           11.217313
## 391           6.214608            8.746785           11.291652
## 392           8.043635            8.988393           12.446925
## 393           8.342167            9.215580           11.053371
## 396           9.117435            9.937107           12.574762
## 401           7.788901            9.099535           11.870329
## 406           8.162205            9.411620           11.866787
## 407           6.214608            8.703114           11.659422
## 411           7.651525            9.722432           12.051265
## 412           8.063083            9.851383           12.062444
## 415           9.398941           10.300221           12.717436
## 416           9.238158           10.268803           12.753989
## 422           7.588236            9.209463           11.616289
## 423           6.214608            7.600902           10.559596
## 425           7.830034            8.716201           10.361974
## 435           6.214608            8.285786           10.111080
## 436           8.913038            9.656781           11.520931
## 437           8.427734            9.242513           11.233202
## 438           6.214608            7.600902           11.886506
## 443           8.408451            9.217838           11.651474
## 446           8.416727            9.224756           11.071337
## 447           6.214608            7.600902           11.749633
## 451           6.214608            7.600902            8.517193
## 452           6.214608            8.247823           11.324304
## 453           6.214608            7.600902           11.207507
## 458           8.824927            9.753283           11.640244
## 464           7.763714            8.945571           11.152768
## 467           6.214608            8.644313           11.443257
## 472           6.214608            7.600902           10.233957
## 473           6.214608            7.600902           10.958889
## 477           6.214608            7.600902           11.750488
## 483           6.214608            9.071623           11.070838
## 490           7.879125            8.947560           11.986073
## 492           7.813023            8.944636           11.986190
## 493           6.214608            9.042515           11.642805
## 494           6.214608            7.600902           10.499668
## 496           6.214608            7.600902           10.790088
## 503           6.214608            7.600902            9.567612
## 506           6.214608            7.600902            9.743786
## 507           6.214608            7.600902           10.461036
## 509           6.214608            7.600902           11.674129
## 514           6.214608            7.600902           10.598166
## 515           6.214608            7.600902           10.604133
## 516           6.214608            9.235699           11.879678
## 517           6.214608            7.600902           10.151737
## 524           8.286215            9.309368           11.414491
## 525           6.214608            9.003960           11.989251
## 527           6.214608            7.600902           10.102998
## 528           8.272062            9.329666           10.996953
## 532           6.214608            7.600902           11.736244
## 533           7.542227            9.347415           12.274247
## 535           6.214608            7.881845           11.502853
## 536           6.214608            7.600902           11.735916
## 549           6.214608            9.199847           11.621114
## 550           6.214608            8.762115           11.582077
## 553           6.214608            8.934498           12.040456
## 555           8.047037            8.960496           10.524734
## 556           6.214608            7.600902           10.711752
## 558           6.214608            8.868397           11.083305
## 559           7.307603            9.161106           11.967532
## 566           7.680437            9.227205           11.962533
## 568           6.214608            7.600902           10.614843
## 575           7.826517            9.174146           11.855074
## 579           6.214608            7.600902           10.719272
## 581           6.214608            8.300403           10.714141
## 583           8.410050            9.356312           11.804939
## 589           6.214608            8.723354           11.039598
## 603           6.214608            7.600902           10.215591
## 604           6.214608            7.600902           11.175055
## 610           7.528257            8.902233           11.557770
## 611           6.214608            9.223907           11.193537
## 614           6.214608            9.247300           11.065914
## 616           6.214608            7.600902           11.435145
## 617           6.214608            8.219160           11.175044
## 619           6.214608            7.600902            9.908590
## 621           6.214608            9.015546           11.179665
## 622           6.214608            7.600902            8.517193
## 625           7.667096            8.661394           11.125750
## 626           8.298073            9.669868           11.689238
## 628           8.667917            9.677794           12.175904
## 630           7.302825            8.877051           12.178056
## 631           8.353743            9.297309           12.074814
## 633           7.248993            8.305587           11.942889
## 636           8.377937            9.444863           12.110319
## 640           8.377199            9.219266           11.630438
## 650           6.214608            7.600902           11.424097
## 652           6.214608            7.600902           11.218783
## 653           6.214608            8.480793           11.897678
## 655           8.543611            9.726839           12.005059
## 657           8.806184            9.911366           11.649747
## 662           8.637076            9.887257           12.038669
## 664           7.727003            8.848025           11.903284
## 669           8.465155            9.487232           11.760764
## 672           7.696905            9.430757           11.302542
## 674           6.214608            7.600902            9.906404
## 677           6.214608            7.600902           11.082701
## 680           6.214608            7.600902           10.044644
## 684           6.214608            7.600902           11.353244
## 686           8.404319            9.213970           11.537854
## 689           6.214608            7.600902           11.631461
## 690           6.214608            9.342903           12.029255
## 691           6.214608            7.600902            9.766293
## 692           6.214608            7.600902           10.506180
## 693           6.214608            7.600902           10.751246
## 694           6.214608            8.550292           10.362523
## 695           6.214608            8.406927           12.220567
## 698           6.214608            8.504138           11.323900
## 702           6.214608            8.116056           11.367252
## 703           8.314647            9.426870           11.951923
## 704           6.214608            8.730921           11.576639
## 705           7.211047            8.584375           11.499355
## 709           8.181549            9.475985           12.018824
## 710           7.770578            9.534857           11.518720
## 711           6.214608            7.600902           12.121454
## 714           6.214608            8.974067           12.111504
## 715           6.214608            7.600902           11.046177
## 718           8.776020            9.846123           12.755944
## 720           8.958326           10.140847           12.606617
## 722           7.244709            8.733907           11.448419
## 723           6.214608            8.108716           10.432981
## 725           7.427104            9.169983           11.932281
## 728           9.059406            9.952497           12.228315
## 730           6.214608            9.077843           12.176568
## 734           6.214608            7.600902           10.778400
## 735           6.214608            7.600902           10.348225
## 741           7.686731            9.241761           11.361600
## 749           6.214608            7.600902            9.667118
## 752           6.214608            8.829316           11.483796
## 753           6.214608            8.536069           11.590320
## 756           8.419697            9.802817           12.350174
## 759           7.169272            8.707020           11.870327
## 762           8.610477            9.546120           12.482512
## 765           7.409318            8.704054           11.350943
## 768           9.107094           10.400889           12.412546
## 769           9.248851           10.081137           12.078749
## 770           6.214608            7.600902           11.517496
## 771           6.214608            7.600902           11.174929
## 785           7.237732            8.280305           10.971330
## 797           8.152622            8.983696           11.737318
## 800           7.792083            9.186338           11.651509
## 805           8.356087            9.901216           11.912306
## 807           8.214226            9.297925           12.232018
## 809           7.653885            9.056176           10.596603
## 814           8.213868            9.167589           11.870266
## 815           6.214608            7.600902           11.880538
## 818           8.822938            9.899348           12.557693
## 820           8.387881            9.536369           12.456182
## 830           8.158263            9.421355           11.287198
## 837           7.705129            9.569466           12.016619
## 838           6.714515            8.267743           11.116330
## 843           7.165778            9.061611           10.963839
## 845           8.064728            9.500226           11.769954
## 851           8.507625            9.374385           11.320729
## 855           8.967770            9.755895           12.019523
## 856           6.897241            9.758872           11.821033
## 857           8.738359            9.872736           11.999244
## 859           8.557831            9.705652           11.416048
## 864           8.276997            9.653574           11.663286
## 870           7.391010            9.541845           11.831020
## 874           6.214608            7.600902           10.044448
##     Log_PrscRdLen_10000m Log_PrscRdLen_15000m Log_PrscRdLen_25000m
## 3              12.840663            13.282656             13.79973
## 5              12.768279            13.189489             13.70026
## 6              12.994141            13.326132             13.85550
## 7              13.278416            13.826365             14.45221
## 8              12.128956            12.753045             13.80017
## 9               9.210340             9.615805             11.89377
## 14             10.420770            12.447722             13.34258
## 16             12.793503            13.281388             13.90072
## 18             12.818512            13.529346             14.10779
## 20             13.232356            13.659840             14.16990
## 24             12.120303            12.521557             13.10635
## 26             11.078097            11.400922             11.82078
## 27             12.390361            12.833780             13.33215
## 28             12.571092            13.213701             13.98699
## 33              9.336948            11.488893             12.11156
## 37             11.705446            12.322732             13.07762
## 42             11.230948            11.666007             12.22026
## 44             11.665526            12.147130             13.64745
## 46             12.204560            12.613562             13.38595
## 47             11.813696            12.213245             12.89298
## 48             11.228268            11.622009             12.64868
## 50             11.711572            12.157880             12.79400
## 52             13.127664            13.657267             14.10463
## 56             12.671614            13.325126             14.07803
## 62             11.049508            11.589992             12.52286
## 65             11.872009            12.302382             12.82163
## 68             11.962187            12.324057             12.85726
## 69             11.861234            12.267776             12.84934
## 72             11.499419            12.141250             13.11922
## 73             10.426984            11.272335             11.94941
## 78             12.193627            12.778735             13.42418
## 80             11.332983            11.915687             12.91542
## 81             12.381661            13.176847             14.19641
## 82             12.999874            13.680282             14.55411
## 89             12.615322            13.474215             14.43659
## 90             11.979379            12.607655             13.38056
## 92             11.873460            12.301434             12.73350
## 93             11.877927            12.563350             13.41588
## 94             11.796774            12.082217             12.55280
## 96             12.799125            13.647049             14.55346
## 99             11.194554            11.730875             12.40230
## 109            12.030751            12.688832             13.30387
## 110            12.627674            13.241419             13.94904
## 111            11.719320            12.138484             12.80342
## 114            11.980769            12.621793             13.53385
## 115            12.624065            13.130622             13.80250
## 117            12.931223            13.599764             14.19471
## 119            12.947196            13.457149             14.00775
## 129            12.596568            13.088190             13.63351
## 130            11.545490            12.012443             12.81410
## 134            11.615201            12.202486             13.11685
## 137            11.883233            12.511229             13.54333
## 139            11.532789            12.138566             13.34646
## 140            11.831047            12.727254             14.25077
## 144            12.409875            13.367230             14.26384
## 148            13.228694            13.839998             14.53036
## 151            10.178253            10.879724             13.01219
## 153            12.220826            12.768768             13.51108
## 154            12.310276            12.721813             13.15811
## 158            12.855318            13.407554             14.22322
## 167            13.190655            13.729250             14.44591
## 172            12.547750            13.302724             14.22158
## 173            13.109153            13.485700             14.08622
## 175            13.187858            13.936505             14.66419
## 177            13.657943            14.143572             14.84688
## 180            13.443043            14.333883             15.19792
## 185            12.613307            12.944777             13.38756
## 193            13.065977            13.574380             14.39669
## 196            12.953848            13.561059             14.27278
## 197            12.784542            13.486986             14.51925
## 200            13.284082            13.896006             14.56871
## 202            11.976625            12.467087             13.09711
## 209            12.295222            12.783223             13.73201
## 213            12.914183            13.384650             13.92079
## 217            13.076403            13.738936             14.58740
## 219            13.169062            14.122864             14.91974
## 220            13.180961            13.873859             14.85812
## 230            13.261553            13.684255             14.17879
## 232            13.060568            13.628275             14.15806
## 233            11.552674            12.323959             13.71120
## 236            13.254755            13.869858             14.56772
## 239            12.414234            12.950974             13.58425
## 240            12.352258            12.809081             13.49297
## 242            11.449951            11.985101             12.69291
## 244            11.326019            11.768369             12.42904
## 245            11.375845            11.737190             12.38742
## 246            12.320260            12.832933             13.57439
## 247            12.547662            12.932230             13.54257
## 253            12.482756            13.404255             14.29918
## 257            12.749302            13.446711             14.41914
## 261            12.114637            13.083833             14.15194
## 264            12.646684            13.209735             14.11713
## 266            11.855375            13.022636             14.06432
## 268            12.461055            13.360672             14.37529
## 273            12.648903            13.134540             13.91820
## 282            12.193886            12.863351             13.62368
## 283            12.343388            12.875070             13.64377
## 287            11.976564            12.681672             13.71448
## 288            11.898468            12.588908             13.46292
## 290            12.520660            13.156319             13.85618
## 300            12.534265            13.205146             13.97430
## 301            12.597040            13.292692             14.10324
## 304            12.576959            13.126360             13.92959
## 311            12.624121            13.189335             14.07243
## 312            12.667272            13.361839             14.05098
## 314            12.739730            13.099067             13.83358
## 315            12.467386            12.942689             13.72632
## 316            12.505198            12.920867             13.70190
## 317            12.480464            12.978102             13.72977
## 320            12.101734            12.674713             13.30423
## 322            12.054315            12.379172             13.30145
## 323            11.394630            12.181386             13.00992
## 325            11.832841            12.280232             12.99728
## 333            12.713839            13.231469             13.81055
## 336            12.677323            13.295432             13.86343
## 337            11.093419            11.607871             12.37246
## 339            11.446388            12.054521             12.81268
## 342            11.662769            12.242168             12.87832
## 351            12.828455            13.397908             14.16385
## 355            12.598644            13.406854             14.43261
## 356            12.853435            13.403536             14.09011
## 359            12.831974            13.302575             14.36063
## 360            13.090214            13.718563             14.52956
## 366            13.386773            13.959105             14.68766
## 368            12.742200            13.386567             14.26234
## 369            12.088944            13.099351             14.17295
## 370            12.660454            13.213372             14.02693
## 373            11.648163            12.006030             13.13966
## 374            12.713573            13.158706             13.72241
## 376            12.666601            13.552381             14.36943
## 377            12.435674            13.411729             14.38637
## 385            13.078701            13.704341             14.29293
## 386            12.459316            13.177539             14.03566
## 391            12.612522            13.486569             14.64136
## 392            13.344755            13.929591             14.75419
## 393            12.661076            13.671651             14.70095
## 396            13.720582            14.325754             15.14823
## 401            13.441016            14.102809             14.94211
## 406            12.896150            13.358457             14.25255
## 407            13.126566            13.866523             14.63702
## 411            13.188202            13.758879             14.43622
## 412            13.180634            13.763941             14.43533
## 415            13.622968            14.169571             14.87127
## 416            13.636922            13.998345             14.85746
## 422            12.467890            12.933698             13.71740
## 423            11.972975            12.440311             13.20817
## 425            10.950715            11.573969             12.22174
## 435            11.353358            11.793238             12.64301
## 436            12.165358            12.837804             13.90726
## 437            11.984902            12.315719             12.90438
## 438            13.119888            13.804053             14.60415
## 443            13.087633            13.676048             14.36676
## 446            12.253257            13.080016             14.19278
## 447            13.182091            13.752096             14.41791
## 451             9.210340            10.656574             11.84227
## 452            12.239378            12.914635             14.13566
## 453            12.616892            13.575661             14.46998
## 458            12.514470            12.966044             13.47354
## 464            12.135537            12.589146             13.05928
## 467            12.552776            13.101886             13.99563
## 472            11.790517            12.539836             13.20103
## 473            12.071597            12.628957             13.30374
## 477            12.610815            13.093836             13.65360
## 483            12.305707            12.974017             13.97700
## 490            12.983360            13.732622             14.56616
## 492            12.982494            13.734761             14.57069
## 493            12.312096            12.628101             13.03606
## 494            11.274264            11.749993             12.49141
## 496            11.474185            11.989702             12.64158
## 503            10.322881            10.755419             11.28567
## 506            10.602660            10.927311             11.36142
## 507            11.893005            12.310445             12.88635
## 509            12.691763            13.390932             13.92494
## 514            12.117148            12.563978             13.21650
## 515            11.264148            12.091956             13.29667
## 516            12.756283            13.291929             13.94893
## 517            11.112111            11.497788             12.38057
## 524            12.435616            13.410041             14.26639
## 525            12.763746            13.235896             14.10300
## 527            12.086833            12.571509             13.19456
## 528            11.815511            12.461983             13.02276
## 532            12.947144            13.694138             14.53733
## 533            13.655658            14.280043             14.95895
## 535            12.902111            13.570488             14.42257
## 536            13.071761            13.935895             14.94461
## 549            12.424062            12.971354             13.85667
## 550            12.962662            13.444690             14.08184
## 553            12.799174            13.457413             14.06260
## 555            11.768228            12.153963             12.75413
## 556            11.820714            12.223747             12.91691
## 558            11.835272            12.168106             12.94270
## 559            12.784925            13.157780             13.58953
## 566            13.129726            13.705625             14.29693
## 568            11.077503            11.584326             12.71212
## 575            13.115564            13.594612             14.25804
## 579            12.217010            13.231509             14.15861
## 581            12.033516            12.908484             13.53435
## 583            13.099758            13.858593             14.64987
## 589            12.425173            13.040119             13.71174
## 603            10.930441            12.281763             13.20098
## 604            12.676964            13.474203             14.33804
## 610            12.363808            12.758289             13.47495
## 611            12.172329            12.770499             13.56817
## 614            11.891498            12.425143             13.22865
## 616            12.780212            13.398637             14.05539
## 617            11.992792            12.430266             13.28358
## 619            11.247002            11.865000             12.43463
## 621            12.392315            12.846759             13.30080
## 622            10.880877            11.627899             12.30162
## 625            12.684551            13.296598             14.24642
## 626            12.615902            13.019048             14.00359
## 628            13.126832            13.644085             14.48284
## 630            13.131813            13.651292             14.49586
## 631            13.147928            13.738306             14.51532
## 633            13.164916            13.773073             14.56912
## 636            13.414307            13.930818             14.56396
## 640            12.857915            13.676599             14.56909
## 650            12.707269            13.395353             14.14077
## 652            12.610600            13.434527             14.26760
## 653            13.359460            13.808634             14.43135
## 655            13.058983            13.641802             14.54000
## 657            12.573004            13.172265             13.98698
## 662            12.775298            13.376557             14.19206
## 664            12.938270            13.471331             14.36254
## 669            12.727402            13.019270             13.53716
## 672            12.360333            12.935514             13.72048
## 674            10.667766            12.239504             13.04956
## 677            12.000031            12.431798             13.00205
## 680            11.256158            12.150173             13.05818
## 684            12.187641            12.602403             13.20961
## 686            12.278015            12.702713             13.17243
## 689            13.247943            13.785964             14.28051
## 690            13.135072            13.668010             14.24483
## 691            11.541530            12.178550             12.91978
## 692            12.218076            12.798730             13.40360
## 693            11.883676            12.648162             13.77107
## 694            11.980321            12.747428             13.89421
## 695            13.308986            13.923856             14.64770
## 698            12.320506            13.238914             14.19972
## 702            12.476076            13.080241             13.96114
## 703            13.141016            13.806508             14.72475
## 704            12.528068            12.991916             13.88838
## 705            12.503221            13.070368             13.98524
## 709            13.210357            13.907252             14.98647
## 710            12.657249            13.118962             13.77154
## 711            13.185547            13.685571             14.31310
## 714            13.235515            13.940207             14.96389
## 715            12.443541            13.306148             14.10947
## 718            13.728352            14.315974             15.07200
## 720            13.744232            14.330857             15.08222
## 722            12.467353            13.101863             13.92134
## 723            11.655058            12.675285             14.15549
## 725            12.777005            13.381695             14.14432
## 728            13.408270            14.064131             14.76618
## 730            13.353299            14.023197             14.76700
## 734            11.889455            12.419496             13.65293
## 735            11.971514            12.722425             13.78799
## 741            12.493704            13.213455             14.06187
## 749            11.120117            11.775255             12.59962
## 752            12.470680            12.894327             13.41007
## 753            12.533682            12.906918             13.55207
## 756            13.277667            13.795636             14.52256
## 759            12.494418            12.814561             13.17241
## 762            13.382559            14.158083             14.76013
## 765            12.496060            12.892563             13.47186
## 768            13.123732            13.580765             14.08156
## 769            12.978608            13.427862             14.04790
## 770            12.848019            13.647474             14.51263
## 771            12.381239            13.245854             14.02191
## 785            11.521304            12.566866             13.43779
## 797            12.736304            13.265014             13.86204
## 800            12.566171            12.960370             13.67187
## 805            13.041529            13.790476             14.65000
## 807            13.714771            14.382836             15.13984
## 809            11.610006            12.860137             13.95557
## 814            13.306938            14.227557             15.01697
## 815            12.871033            13.298857             13.99630
## 818            13.679190            14.255474             14.88337
## 820            13.573483            14.032905             14.55834
## 830            11.910312            12.672097             13.82077
## 837            12.986520            13.519000             13.93904
## 838            12.043696            12.482925             13.58034
## 843            12.613552            13.307428             13.89984
## 845            12.849188            13.205893             13.69659
## 851            12.362967            13.005690             13.70417
## 855            12.905547            13.411859             14.12447
## 856            12.922130            13.444615             14.17626
## 857            12.910432            13.426439             14.12068
## 859            12.204337            12.773611             13.60872
## 864            12.628501            13.280358             14.33197
## 870            12.647663            13.058806             13.51581
## 874            10.909851            11.478413             12.08479
##     Log_NEI_PM25_Sum_10000m Log_NEI_PM25_Sum_15000m Log_NEI_PM25_Sum_25000m
## 3               6.573127301             6.581917457             6.875899578
## 5               3.772775514             3.785646441             4.160506364
## 6               0.909136688             3.174609213             3.190007668
## 7               7.987614168             8.438952213             8.651068360
## 8               5.412954990             6.643477321             7.806772886
## 9               0.002167007             0.002167007             6.362328519
## 14              0.000000000             4.008887068             6.425888035
## 16              6.048930476             6.233243618             6.430599790
## 18              3.704733653             3.990921996             7.215941444
## 20              5.514308113             5.514316235             5.581576769
## 24              3.736211829             3.736211829             5.889598800
## 26              0.095002496             0.459928419             4.954749959
## 27              3.806774950             3.806774950             4.009038112
## 28              1.679262359             4.157284985             4.262179249
## 33              5.600783800             5.600785697             5.600785697
## 37              3.469949250             3.469949250             4.025981256
## 42              4.459412758             4.459412758             4.464942181
## 44              0.415369656             4.921060227             7.007710124
## 46              2.979051282             3.682215047             4.798589937
## 47              3.934657901             3.954340731             5.591541212
## 48              0.749827071             0.749827071             1.910980767
## 50              3.499172352             3.499208906             3.524718296
## 52              5.499730906             5.604378483             5.651115063
## 56              1.368298538             1.433274393             3.986610956
## 62              0.154064439             0.922895296             6.059470875
## 65              4.280346515             4.964590561             5.126055482
## 68              5.387386184             5.557637424             5.614321909
## 69              5.383221344             5.387471994             5.614322970
## 72              4.195927963             4.389649474             4.482636658
## 73              0.877392590             0.877392590             2.421967650
## 78              4.885185476             5.768562126             6.031923352
## 80              3.855345818             3.855421829             4.193862181
## 81              3.767384675             4.661884865             5.236752554
## 82              4.457533974             6.742035970             7.011774601
## 89              6.611604485             6.991348429             7.452689651
## 90              3.565715550             4.719002427             6.563942254
## 92              2.495388607             3.176587483             4.001385870
## 93              3.159385007             3.550529268             5.140060167
## 94              1.818780506             2.266814933             2.550841174
## 96              4.254478808             4.647467621             6.120918757
## 99              3.706307682             3.710947514             3.712345740
## 109             0.333271620             0.790632469             3.812139538
## 110             4.545647131             4.855984697             5.942601711
## 111             5.120156544             6.845472149             7.157636535
## 114             5.516661282             5.742584323             6.248635449
## 115             5.752360839             5.936771607             6.259767190
## 117             6.701289647             6.788966506             6.902244553
## 119             5.154102699             6.171574614             7.151224200
## 129             4.694240615             5.405961012             5.995506916
## 130             0.830393044             2.115144738             4.394847811
## 134             2.843032172             3.481156246             4.102655981
## 137             2.702347687             3.235086472             4.133604173
## 139             0.769992891             1.251368594             3.772860085
## 140             1.712440732             3.368254820             4.625074703
## 144             4.824669308             5.072107311             6.891603751
## 148             6.357162282             7.385544009             7.626139935
## 151             0.006109714             0.407891699             2.945357611
## 153             4.764630929             4.899861348             5.910492678
## 154             4.131257887             4.470929755             5.168164254
## 158             5.130360868             5.145554399             5.247960712
## 167             3.484239567             3.493713139             4.061742582
## 172             0.054154153             1.376569712             4.654352001
## 173             4.532919982             4.575876892             4.658805066
## 175             6.163505035             6.281171646             6.675887099
## 177             6.406647329             7.202787120             7.815910531
## 180             4.886809658             5.004692084             5.179764784
## 185             1.478704684             2.010127692             2.164313007
## 193             6.266489943             6.990490938             7.477499801
## 196             3.783080227             3.786106642             5.141393336
## 197             5.249652307             5.946310992             6.671739304
## 200             3.060480638             4.779939380             6.919101312
## 202             7.501523603             7.501583897             8.282657208
## 209             0.006486985             1.716070459             4.754512453
## 213             5.370455363             5.384921118             5.384970969
## 217             0.599462851             1.594639095             5.582623395
## 219             1.269549668             5.946357992             6.415415464
## 220             1.350792727             2.065368875             5.474794266
## 230             5.514308113             5.514308113             5.581573488
## 232             5.304703651             5.514309762             5.581570310
## 233             0.000000000             0.092996168             7.603078995
## 236             4.518914831             5.429569704             5.665729872
## 239             1.883280924             1.996630283             4.942208432
## 240             1.884146867             1.884476465             4.934775958
## 242             0.088461947             0.088461947             0.091297713
## 244             0.218495146             0.218495146             0.219159678
## 245             0.084799427             0.084799427             0.084799427
## 246             4.366633590             5.398010459             5.406707081
## 247             3.529295654             3.664229181             4.051929792
## 253             6.856031200             7.479731872             9.090230180
## 257             6.851128031             7.019112747             7.889767904
## 261             3.681638328             5.496190002             6.870989934
## 264             3.442058504             3.660000510             5.225625872
## 266             2.974775196             5.868389000             6.090071611
## 268             2.815497291             3.496809099             4.819159200
## 273             5.704387676             7.298788327             7.639313627
## 282             0.417008840             1.246377304             6.029156485
## 283             5.767740081             5.852841217             5.944812262
## 287             4.433214773             4.434768897             4.998682066
## 288             4.369998030             4.559133339             5.077841582
## 290             4.675098070             4.776292672             6.149942505
## 300             8.118192372             9.229082590             9.606587474
## 301             8.822477885             9.328953737             9.337806116
## 304             0.853728117             0.874143422             4.867586034
## 311             5.635468925             5.645066500             6.392102966
## 312             5.641293898             5.656983290             6.203353802
## 314             6.855981385             6.855983961             6.856036509
## 315             3.759746945             6.454794951             8.900104574
## 316             3.759746945             5.017374758             8.900066773
## 317             3.759746945             3.946017104             8.900104574
## 320             5.026283660             5.146878815             5.163784964
## 322             6.599391378             6.603477759             6.614032933
## 323             0.000000000             0.017009384             1.788662155
## 325             5.599036896             5.601542276             5.676356023
## 333             6.288727476             7.318697281             7.346588731
## 336             5.629017966             6.438758810             6.810990858
## 337             0.169222158             0.169222158             0.170797435
## 339             0.002167007             0.013459924             4.811925195
## 342             0.013570838             0.559342631             5.416596712
## 351             7.287054486             7.733272622             8.001968871
## 355             0.000000000             3.744616784             4.879494283
## 356             5.541500054             5.547528738             6.632659668
## 359             3.556304798             3.596999050             5.309047192
## 360             4.641018615             4.779323170             4.921053997
## 366             4.873540691             6.218672523             9.024879677
## 368             4.635122014             5.771487937             5.943282488
## 369             8.225869079             8.256212350             8.331916362
## 370             2.428155209             3.243998189             5.367863220
## 373             0.887411801             0.888304570             7.654277584
## 374             7.605223858             8.304911992             8.307139220
## 376             7.447663061             8.564736581             8.797821373
## 377             8.022259746             8.122203154             8.931433156
## 385             7.123143907             7.205381810             7.571757279
## 386             0.631294397             4.966473470             5.419010641
## 391             1.876112364             1.943317165             5.121159995
## 392             6.941086722             8.313812627             8.326379376
## 393             0.837257138             3.791137359             6.311349925
## 396             3.434737551             4.423124070             5.182636365
## 401             3.118628526             5.103637950             8.318861576
## 406             5.185763314             5.230419823             5.475146838
## 407             4.144978914             5.302024558             6.359496317
## 411             5.116895283             5.396592986             5.698299312
## 412             5.116895283             5.396509207             5.697120862
## 415             6.122324592             6.217385290             6.498426027
## 416             6.145962179             6.248485003             6.483552531
## 422             8.414197109             8.417221452             8.500717094
## 423             2.130839348             3.891810879             4.457796185
## 425             0.062465092             0.062465092             0.271520144
## 435             0.347297617             0.347297617             0.442872553
## 436             7.261550380             7.519585574             7.899954666
## 437             6.567722655             6.778345412             6.951744675
## 438             2.877544333             4.685565040             7.337815320
## 443             7.176144908             7.201895723             7.743216123
## 446             3.556405834             4.489344246             5.397904517
## 447             7.167310521             7.202393768             7.746997997
## 451             0.000000000             0.000000000             2.055313219
## 452             5.151858147             6.136924240             7.430503866
## 453             5.605548591             6.624480342             7.642240423
## 458             4.274532392             4.494166109             4.613106053
## 464             5.269426689             5.751141154             6.317614460
## 467             5.162713314             5.238036233             6.024528867
## 472             3.533286635             3.719824390             4.656178229
## 473             5.940580914             5.940762170             5.947747807
## 477             5.150509752             5.160156738             5.160157533
## 483             5.086514979             5.311426636             7.001306655
## 490             6.856337049             6.951359849             7.695155915
## 492             6.850460792             6.948068000             7.716709222
## 493             3.923202408             3.970926066             3.971640813
## 494             5.302972750             5.306314284             5.488738612
## 496             3.556762044             3.748441702             5.490639529
## 503             3.633300816             3.633300816             3.633325118
## 506             0.054233174             0.054233174             1.329276955
## 507             4.869186392             5.140853868             5.140853868
## 509             5.463298438             7.335364339             7.346632501
## 514             3.326341691             3.326341691             3.358309785
## 515             3.780263466             3.780282600             4.446848952
## 516             5.168927425             5.695584774             5.904082148
## 517             1.661804612             1.661804612             3.299568830
## 524             6.162363706             6.249846981             6.297188412
## 525             7.958732595             7.958822153             7.967774004
## 527             2.256290693             3.195499898             5.118378279
## 528             2.183969443             3.064068964             5.119198586
## 532             7.755151494             8.102192048             8.192914028
## 533             6.750109173             7.042209251             7.586223900
## 535             6.300529849             8.075823517             8.326661480
## 536             6.938756597             7.886184995             8.093481132
## 549             4.201587027             6.761799672             7.034162709
## 550             3.592434729             4.182623377             5.638920549
## 553             3.698912191             5.193796372             5.900681879
## 555             0.025445761             0.116533104             0.171375323
## 556             0.215433908             0.372609282             3.900212848
## 558             1.782971837             2.107623905             6.749680772
## 559             0.259674551             0.695249451             0.695249451
## 566             4.181865969             4.551729690             4.781302348
## 568             0.001081405             0.001081405             0.169380012
## 575             3.816684934             4.272323085             4.319380742
## 579             6.800054866             7.006477001             8.329047369
## 581             1.352040095             1.352263173             3.620056584
## 583             2.822191345             3.952567193             6.717215816
## 589             4.113891183             4.869311518             4.938749519
## 603             1.437462648             6.303561819             6.306113866
## 604             4.346902641             5.048061501             8.109331963
## 610             2.739944479             2.739953420             3.073207311
## 611             2.726523269             2.726523269             2.766292452
## 614             0.099009674             0.099009674             4.315093510
## 616             4.697407129             4.869170514             5.052666449
## 617             0.824796643             0.825747073             0.860126401
## 619             0.000000000             0.000000000             0.970021054
## 621             5.994674963             6.014952199             6.015906665
## 622             6.667263184             6.732128773             6.732145235
## 625             4.731278126             5.348458155             7.510993585
## 626             2.543212454             2.597021636             4.907497617
## 628             7.072275617             7.277095744             7.321823846
## 630             7.072275617             7.281054973             7.321823846
## 631             7.058682831             7.158419640             7.322215757
## 633             7.054353137             7.155492024             7.321822222
## 636             5.889034298             6.233488023             6.322110628
## 640             5.748938979             6.093271798             6.460665105
## 650             7.082273846             7.301031298             7.469344146
## 652             7.506756049             7.522130353             8.047888974
## 653             5.720003664             6.953206631             7.633493436
## 655             5.025593921             6.101849438             7.071476549
## 657             4.447384983             5.457706746             6.254990913
## 662             6.466764187             6.554321077             6.567318872
## 664             4.923423244             4.960390939             5.417175345
## 669             6.812929047             6.813056372             6.813213123
## 672             0.148689587             0.148808918             4.527990467
## 674             4.202792510             4.202815804             4.203933740
## 677             1.018144947             1.121711365             1.167098952
## 680             0.195065515             4.163589109             5.307171179
## 684             4.960126676             6.951998208             6.996873823
## 686             6.903994515             6.980811678             6.996866983
## 689             5.683997424             6.157651365             6.790406547
## 690             5.969693661             6.334491981             6.789281996
## 691             1.599195712             3.436219368             3.436276852
## 692             1.200567011             2.034981991             2.035092367
## 693             1.495973287             1.530759645             6.075432621
## 694             0.060098156             2.637732114             4.464040361
## 695             5.896203752             7.131096365             8.084639096
## 698             6.870421838             6.957894036             7.151692612
## 702             7.273924935             7.322386440             7.409625056
## 703             4.637611862             7.577750416             7.709357547
## 704             3.706860830             4.024357993             7.333051286
## 705             2.221998824             4.363872627             4.460521217
## 709             7.494458855             7.558417411             8.119688597
## 710             4.447482092             4.453804172             4.492537183
## 711             5.601264792             5.612551010             5.694359333
## 714             3.731969416             4.345426275             7.241276512
## 715             5.662274882             6.940066534             7.111137936
## 718             6.752939248             7.451338130             7.735841753
## 720             6.950690801             7.015902661             7.569157262
## 722             3.215477251             3.222047007             5.806495193
## 723             2.460065920             4.416388599             9.537863652
## 725             4.656941061             5.298587899             8.735032841
## 728             3.365888617             4.631729575             5.744869246
## 730             3.385097313             4.648270257             5.784293200
## 734             0.071989909             0.134425380             2.213154926
## 735             0.652065686             3.428468129             4.822645078
## 741             1.185311751             4.208276619             6.794512509
## 749             0.002167007             0.002167007             0.002305168
## 752             0.004329329             0.004921094             0.682578339
## 753             0.004329329             0.680738736             0.683673941
## 756             5.614376929             5.642977775             5.683888895
## 759             4.441669770             4.705256348             6.632509938
## 762             5.385174166             5.733357474             6.253136433
## 765             6.659765658             6.677332216             6.769168366
## 768             5.776786893             5.782541315             5.951056182
## 769             5.147659810             5.782536805             5.832695502
## 770             4.685924602             5.227216281             7.769601877
## 771             7.895737741             8.258480284             8.634848794
## 785             0.383203882             0.383203882             0.674013335
## 797             0.000000000             2.609794114             4.405052221
## 800             3.841171059             3.841754695             3.841857004
## 805             6.635072818             6.725870939             7.271740342
## 807             2.801258311             4.946637691             5.365319687
## 809             2.502148747             3.447916511             5.840762459
## 814             3.515376495             3.580545308             4.021621037
## 815             3.056875628             3.067048704             5.017088309
## 818             5.799665004             5.920499965             6.171463785
## 820             5.068875914             5.369527344             6.315942422
## 830             5.724272838             5.736400517             6.270225059
## 837             4.635643881             4.755125788             8.250426011
## 838             4.485187652             4.485313086             7.705408358
## 843             7.952987548             8.015237332             8.406191761
## 845             5.191577890             5.276010226             5.283135099
## 851             1.923555192             2.765531758             3.045873032
## 855             5.171638561             5.265992529             5.607838153
## 856             5.107208394             5.228729189             5.574462547
## 857             4.953683985             5.256643524             5.622880402
## 859             1.768948308             5.115325846             5.242296030
## 864             3.562707181             3.811794671             5.444018358
## 870             6.764033982             6.764033982             6.789201836
## 874             0.002167007             0.106249031             0.106249031
##     Log_NEI_PM10_Sum_10000m Log_NEI_PM10_Sum_15000m Log_NEI_PM10_Sum_25000m
## 3               6.691873127             6.701277408              7.14885842
## 5               4.437198843             4.462679325              4.67831103
## 6               0.928888905             3.674739043              3.74462870
## 7               8.209759579             8.648834554              8.85801911
## 8               5.771181130             6.868896765              8.02107151
## 9               0.016549626             0.016549626              6.89199158
## 14              0.000000000             4.016695044              6.96158011
## 16              6.230905819             6.427890313              6.64032578
## 18              3.939083577             4.229315143              7.33132719
## 20              5.712067870             5.712077632              5.78626709
## 24              3.879107227             3.879107227              6.61394661
## 26              0.623242822             1.721041539              5.47910147
## 27              3.881124278             3.881124278              4.07076879
## 28              1.761445434             4.277644933              4.76013767
## 33              6.374419098             6.374425609              6.37442561
## 37              4.251442675             4.251442675              5.10885255
## 42              5.171147507             5.171147507              5.19186458
## 44              1.601608644             4.986761370              7.32259063
## 46              3.124916053             3.786380064              4.91402286
## 47              3.972470041             3.991565279              6.72893640
## 48              1.344056790             1.344056790              2.18602982
## 50              3.640357549             3.640601688              3.67198158
## 52              6.352010627             6.445752853              6.46671681
## 56              1.766226226             1.821161371              4.39704822
## 62              0.824735519             1.406410010              6.30935018
## 65              4.920492658             5.424792063              5.57117902
## 68              5.539774020             5.723682180              5.79190017
## 69              5.534704807             5.539847835              5.79190107
## 72              4.837930403             5.077206511              5.23953068
## 73              2.134166441             2.134166441              2.92154216
## 78              5.037645284             5.840860360              6.14283048
## 80              4.261139465             4.261228315              4.71283417
## 81              4.594150316             5.212957258              5.73870926
## 82              4.764171414             7.225814169              7.45712516
## 89              6.789814991             7.153831447              7.60937827
## 90              4.505033869             5.292333685              8.20435889
## 92              2.919602647             3.734306469              4.49454263
## 93              4.674096097             4.796928979              5.57819605
## 94              2.361733302             3.505414896              3.63693979
## 96              4.558390170             4.970542976              6.36896504
## 99              3.852492982             3.877796344              3.88554757
## 109             1.396864549             1.666835564              4.93459512
## 110             5.214152768             5.542568741              6.43236149
## 111             5.759777383             7.391473191              7.75233355
## 114             5.739107291             6.046557139              6.57215607
## 115             5.935754141             6.096735355              6.51827279
## 117             6.853830317             6.949341443              7.07617188
## 119             5.371998228             6.340357776              7.31331027
## 129             5.299135402             5.780236279              6.36459696
## 130             0.925287536             2.708574385              4.90249846
## 134             3.279421510             4.481874064              4.97456371
## 137             3.199038472             3.891333189              4.98392388
## 139             0.780198898             1.690894353              4.03145006
## 140             2.742852849             3.689386058              5.08755692
## 144             5.708932959             5.964888754              7.57884867
## 148             7.088899534             7.999446793              8.25163433
## 151             0.046064300             1.017366969              3.90812481
## 153             5.388681313             5.634148405              6.62669935
## 154             5.048768615             5.471389204              6.24944277
## 158             5.279624730             5.292944255              5.38342347
## 167             3.580554576             3.592051955              4.19772925
## 172             0.142460316             1.724539588              4.78351854
## 173             4.630796678             4.706238327              4.78165654
## 175             6.169852302             6.301066753              6.73817278
## 177             6.623931681             7.317211079              7.95047924
## 180             4.989893264             5.102184716              5.35445199
## 185             2.499991644             2.850452375              3.01205478
## 193             6.559756016             7.276005069              7.88999414
## 196             4.270496133             4.278908627              5.49518811
## 197             5.350374602             6.076783738              6.85264357
## 200             3.526212765             4.957774810              7.06555311
## 202             7.560652272             7.561089361              8.32975951
## 209             0.048849201             2.537601139              4.90525151
## 213             5.945309458             5.954825317              5.95492074
## 217             1.989648685             2.347396195              6.35543187
## 219             1.305967140             5.962198100              6.80331599
## 220             2.750564493             2.984805476              6.24647394
## 230             5.712067870             5.712067870              5.78624652
## 232             5.336707155             5.712036775              5.78622660
## 233             0.000000000             0.559429628              8.35634292
## 236             5.003169190             6.037200743              6.22249610
## 239             2.645634032             3.003840496              5.54583175
## 240             2.648738397             2.649918170              5.51418855
## 242             0.537360001             0.537360001              0.55120772
## 244             1.057264055             1.057264055              1.05947188
## 245             0.519245192             0.519245192              0.51924519
## 246             5.443771772             6.007298509              6.02710022
## 247             4.147557065             4.537125918              4.92224375
## 253             7.300200294             7.908303166              9.39436185
## 257             7.299862691             7.459809894              8.26039330
## 261             4.097509081             5.787684128              7.40940208
## 264             3.921224494             4.174089564              5.61584826
## 266             3.257357701             7.028424403              7.14813557
## 268             3.527729758             4.044873892              5.18648720
## 273             6.024391729             7.419808056              7.88562398
## 282             0.512020568             2.106748175              6.22576485
## 283             6.139115867             6.261361328              6.39891241
## 287             4.587870339             4.598067931              5.09606948
## 288             4.530740713             4.696749800              5.16703624
## 290             5.056078758             5.138511805              6.40233066
## 300             8.207533143             9.443283303              9.87342277
## 301             9.089064457             9.535923297              9.54517885
## 304             1.378374573             1.468111215              5.01431307
## 311             5.884597645             5.901072044              6.60272315
## 312             5.894289266             5.915739615              6.45068394
## 314             7.449770938             7.449781881              7.44999891
## 315             4.578657995             6.767244512              9.30205927
## 316             4.578657995             5.544963527              9.30190997
## 317             4.578657995             4.729142504              9.30205927
## 320             5.145132681             5.253210355              5.27243084
## 322             7.022201333             7.025552024              7.03631759
## 323             0.000000000             0.123950847              1.80767387
## 325             5.934127410             5.942183655              6.00669714
## 333             6.564695761             7.702005122              7.73683060
## 336             5.977259942             6.762675294              7.21054837
## 337             0.193687675             0.193687675              0.20545219
## 339             0.016549626             0.099155260              5.04077619
## 342             0.099938181             1.929805121              6.20382297
## 351             7.472248201             7.879971317              8.14369128
## 355             0.000000000             4.066215064              5.35934221
## 356             5.926274373             5.940494604              7.19679491
## 359             3.980241651             4.007823896              5.72839804
## 360             4.989703590             5.141662095              5.31810134
## 366             5.147044079             6.471098509              9.11958164
## 368             4.940290723             5.984068026              6.23454544
## 369             8.330497300             8.371870190              8.49166110
## 370             2.885467124             3.576323296              5.84430246
## 373             0.887411801             0.894258814              7.77007078
## 374             7.678556514             8.574820437              8.57700982
## 376             7.530725589             8.616443178              9.01977623
## 377             8.106066380             8.204321019              9.09015313
## 385             7.246242299             7.375946441              7.72330715
## 386             1.937350668             5.185780270              5.63659203
## 391             2.576296850             2.616515325              5.73988574
## 392             7.394639022             8.628553369              8.63992977
## 393             1.001942147             4.078998639              6.36776727
## 396             3.516679695             4.499209123              5.40779760
## 401             3.189317151             5.720812312              8.62609359
## 406             5.530092936             5.587840005              5.85996520
## 407             4.386830925             5.475096040              6.55675958
## 411             5.492432777             5.815617032              6.17864668
## 412             5.492432777             5.815559547              6.17497310
## 415             6.311478418             6.404575989              6.75590036
## 416             6.327737833             6.430503191              6.71214423
## 422             9.004242475             9.008636736              9.08186171
## 423             3.922236288             4.560811963              4.93167695
## 425             0.402677894             0.402677894              0.67183416
## 435             1.685515723             1.685515723              1.86980759
## 436             7.873409829             8.030833139              8.37809467
## 437             6.990624209             7.135258073              7.29255223
## 438             3.049364875             4.856877838              7.56668617
## 443             7.427492638             7.453066113              8.05912632
## 446             3.880523771             4.961650663              6.00158185
## 447             7.418461991             7.451013248              8.07952968
## 451             0.000000000             0.000000000              2.21850382
## 452             5.982976957             6.607280837              7.75944843
## 453             6.224532751             7.070990108              7.97923012
## 458             5.086196330             5.270944212              5.32801676
## 464             5.995746553             6.453324181              6.83239499
## 467             5.764801290             5.811707439              6.54289053
## 472             3.737535022             4.009890540              5.21287875
## 473             6.804796803             6.807221456              6.81380293
## 477             5.212980975             5.223479137              5.22348488
## 483             5.154758502             5.462745147              7.38596162
## 490             7.458328990             7.521933650              8.06441449
## 492             7.454645982             7.519379552              8.07211393
## 493             4.536885474             4.695759743              4.69622453
## 494             5.611799396             5.620733765              5.85762835
## 496             4.079509100             4.382925114              5.86576717
## 503             4.233539431             4.233539431              4.23364200
## 506             0.356763813             0.356763813              1.45000483
## 507             6.430778668             6.495766163              6.49576616
## 509             5.804591551             7.724450993              7.73692356
## 514             5.141261662             5.141261662              5.14673384
## 515             4.155584466             4.155685590              4.88153108
## 516             5.434418923             6.072156328              6.41955201
## 517             2.151145234             2.151145234              4.34510958
## 524             6.454873305             6.531882187              6.57090365
## 525             7.990242971             7.990910317              8.00011841
## 527             2.499426615             3.674255034              5.30384393
## 528             2.239009535             3.364111690              5.30907425
## 532             7.784971551             8.143819121              8.24207217
## 533             6.847828235             7.142702736              7.73300509
## 535             6.471343096             8.111880421              8.38484447
## 536             7.167614420             8.003512856              8.23020862
## 549             4.518302789             7.071970083              7.38838411
## 550             4.402106697             4.919025199              7.07040587
## 553             4.052773804             5.335298668              6.03144795
## 555             0.180860540             0.899855637              1.06792747
## 556             0.215433908             0.842504552              4.08345303
## 558             2.309625996             2.617365637              6.79367211
## 559             0.482464414             1.953541976              1.95354198
## 566             4.496979836             4.981865970              5.22655192
## 568             0.008288545             0.008288545              0.88367312
## 575             4.268215695             4.666749178              4.71095271
## 579             6.870451457             7.077922536              8.38081533
## 581             1.840087319             1.841140195              4.06334930
## 583             2.893272451             4.271298144              6.82509922
## 589             4.236709862             5.323690921              5.38082825
## 603             1.437462648             6.441596119              6.44630903
## 604             4.513968317             5.218327830              8.26051230
## 610             3.028575262             3.028626798              3.44629662
## 611             3.015915488             3.015915488              3.18981564
## 614             0.288748803             0.288748803              4.32769471
## 616             5.434974856             5.607974507              5.72996904
## 617             1.577656291             1.581095609              1.63987967
## 619             0.000000000             0.000000000              0.97002105
## 621             6.428301982             6.448820516              6.45158853
## 622             7.288552890             7.423456551              7.42351998
## 625             5.103160210             5.580362810              7.58587125
## 626             2.564878088             2.912814377              5.37828917
## 628             7.244816515             7.443317320              7.49321485
## 630             7.244816515             7.447087728              7.49321485
## 631             7.233390219             7.318375742              7.49353588
## 633             7.229745306             7.315834334              7.49320432
## 636             6.052042439             6.427906284              6.52518238
## 640             5.927612937             6.284088173              6.72683518
## 650             7.293942245             7.477070844              7.66449451
## 652             7.795568806             7.818158791              8.42774779
## 653             5.927359690             7.064400645              7.91026223
## 655             5.163845047             6.303530939              7.42672732
## 657             4.598832748             5.711995736              6.58332048
## 662             6.542548788             6.723472781              6.73746218
## 664             5.076713547             5.155712632              5.65853835
## 669             7.232565783             7.233209378              7.23400126
## 672             0.637953516             0.638516154              5.04414649
## 674             4.967247511             4.967330933              4.97132875
## 677             1.116395778             1.682182265              1.86777206
## 680             0.250702483             4.242070851              5.51833281
## 684             5.152349471             7.173489418              7.21189121
## 686             7.119037686             7.196058940              7.21184877
## 689             5.777855316             6.414364061              6.95787374
## 690             6.125881666             6.464799044              6.96958788
## 691             1.970038674             3.675235645              3.67558377
## 692             1.221953184             2.533874604              2.53439005
## 693             2.928310206             2.991295083              6.23654052
## 694             0.072254631             2.676828991              5.09009725
## 695             6.119751482             7.275317867              8.26239635
## 698             7.008301282             7.089080169              7.29191938
## 702             7.368793520             7.571512222              7.67932315
## 703             4.884678468             7.619275647              7.77796153
## 704             3.859737364             4.212338433              7.63585683
## 705             3.100492160             4.711253069              4.94780129
## 709             7.636668031             7.696641947              8.26393259
## 710             4.708922040             4.727562972              4.78831215
## 711             5.625260279             5.637569749              5.79072413
## 714             4.022456275             4.571309622              7.43455534
## 715             6.090778103             7.278450682              7.43094883
## 718             6.848372063             7.572938006              7.89761042
## 720             7.051803514             7.117160331              7.71624966
## 722             3.473397713             3.487097458              6.19049898
## 723             2.462625745             4.596766883              9.67494332
## 725             5.219574715             5.795919844              8.80544703
## 728             3.855217496             4.814496255              6.02898038
## 730             3.876612913             4.860997005              6.12312852
## 734             0.453740219             0.745153121              2.86162509
## 735             1.128354547             3.808300211              5.06819518
## 741             1.199932685             4.585680895              6.86976320
## 749             0.016549626             0.016549626              0.01759675
## 752             0.032829816             0.034302869              1.41014974
## 753             0.032829816             1.404045931              1.41421495
## 756             6.148220808             6.208393683              6.24907426
## 759             4.537450161             4.779646113              7.16550840
## 762             5.410691695             5.827087806              6.46269820
## 765             6.775773299             6.795221305              6.98941572
## 768             5.850714734             5.903955271              6.16430773
## 769             5.289078694             5.903951178              5.96893388
## 770             4.837024579             5.507763222              7.91103169
## 771             7.983015452             8.331455366              8.73720942
## 785             1.521124306             1.521124306              1.64122484
## 797             0.000000000             2.961082274              5.62274142
## 800             3.957857514             3.961845766              3.96254349
## 805             7.383653953             7.432245070              7.83737200
## 807             2.829106087             5.037094544              5.47609007
## 809             3.620979540             4.324957151              6.71340199
## 814             4.269053107             4.446215260              4.69762958
## 815             3.342922750             3.400329803              5.09860317
## 818             6.398766582             6.472360901              6.71274581
## 820             5.096612058             5.398340732              6.33991384
## 830             6.588028561             6.605181633              6.98729714
## 837             4.900940822             4.994026168              8.32092847
## 838             4.943589332             4.944199269              8.14230668
## 843             8.058963040             8.147136594              8.58774234
## 845             6.663096277             6.704355118              6.70982594
## 851             3.398378647             3.788011919              4.54738075
## 855             5.992602346             6.096753644              6.63590621
## 856             5.936783850             6.061438334              6.59471725
## 857             5.874635444             6.123025958              6.66019714
## 859             2.422384406             5.864170528              6.01074009
## 864             4.296595399             4.714434224              6.38561606
## 870             6.914498701             6.914498701              6.95279250
## 874             0.016549626             0.621811988              0.62181199
##     popdens_county popdens_zcta   nohs somehs    hs somecollege associate
## 3       35.4608142 5.408870e+02  7.300 15.800 30.60        20.9     7.600
## 5       75.3670384 1.301037e+02  4.300 13.300 27.80        29.2    10.100
## 6       67.6196640 1.857392e+02  5.800 11.600 29.80        21.4     7.900
## 7      228.7776327 3.345760e+02  7.100 17.100 37.20        23.5     7.300
## 8      228.7776327 9.708881e+01  2.700  6.600 30.70        25.7     8.000
## 9       56.8616114 9.593671e+00 11.100 11.600 46.00        17.2     4.100
## 14     228.7776327 5.995258e+01  9.700 21.600 39.30        21.6     5.200
## 16     129.6994555 4.962453e+02  3.000 17.100 39.00        22.4     6.600
## 18     112.9204615 1.693566e+02  8.800 19.300 36.00        20.2     4.600
## 20     338.8169052 7.494223e+02  8.600 24.600 27.70        19.4     4.300
## 24      32.7072704 8.061103e+01  5.700 14.300 37.60        21.3     7.300
## 26       8.2250282 5.351563e+02 32.700 11.800 45.00         7.9     2.600
## 27       2.7875053 3.622359e+03  1.700  0.000 22.30        36.4    14.700
## 28     160.1928537 2.578344e+03 23.900 17.400 27.30        20.8     4.300
## 33       5.8066084 2.076591e-01  8.600 27.000 35.20        21.0     4.900
## 37      27.0399026 1.860656e+02  3.200  6.500 32.10        30.3    10.200
## 42       5.1930520 1.233559e+01  5.400 13.100 41.70        21.3     5.900
## 44      32.2313135 8.428218e+01  3.600 12.200 28.70        28.2     5.400
## 46      54.7006637 1.102860e+02  6.500 11.400 31.20        21.9     7.800
## 47      10.9611305 1.348316e+01  9.800 15.300 44.40        17.4     4.900
## 48      12.0754263 2.392386e+01  7.300 16.800 29.80        22.1    14.600
## 50      29.3439194 8.871535e+02  6.200  9.800 33.10        20.6     6.000
## 52     194.5077727 4.439959e+02  4.500  9.400 23.60        20.2     4.900
## 56      83.2342134 3.114416e+02 17.700 16.200 31.30        16.9     4.000
## 62      17.2525020 1.862349e+01  2.100  6.400 35.00        21.0    15.800
## 65      60.2969592 2.449266e+03 19.900 16.700 26.50        23.0     6.900
## 68      14.5679417 1.313826e+03  3.400  9.000 28.70        27.6     8.900
## 69      14.5679417 1.313826e+03  4.000  8.600 27.30        25.8     9.800
## 72      16.1340771 1.681611e+02 17.400 14.700 20.40        23.8     7.900
## 73       0.7033431 1.989746e+01 25.000  0.000  0.00         0.0     0.000
## 78      39.8655559 2.477371e+03 18.200 17.900 27.20        23.1     6.100
## 80      19.8710752 5.191128e+01  3.800  8.200 30.00        27.1     9.100
## 81     934.2270959 1.361138e+02 13.700  7.900 25.60        21.4     8.100
## 82     934.2270959 3.289866e+03 13.700  6.500 21.60        25.1     6.100
## 89     934.2270959 4.759523e+03  6.700  4.500 18.60        22.3     8.800
## 90     934.2270959 8.553330e+02  8.900 11.700 27.90        28.5     9.200
## 92      51.0406477 2.503783e+02  8.900 10.000 23.50        26.7     9.500
## 93      48.8491845 1.756141e+03 20.400 10.700 25.10        20.7     8.500
## 94      39.8142883 1.514798e+02  2.200  7.100 23.30        28.9    10.400
## 96    1470.1549190 4.735472e+03 16.000 13.200 29.10        18.5     6.000
## 99       3.0257016 2.278377e+01  1.800  6.800 19.90        35.8    14.600
## 109     15.3664053 3.295319e+01 16.900  9.700 23.60        23.5     8.900
## 110     39.1784128 2.715956e+03 17.300 12.300 27.50        22.5     6.400
## 111     39.1784128 9.572534e+02  8.600 14.300 29.50        26.5     8.300
## 114     39.1784128 5.551599e+02 24.100 21.900 28.20        15.5     2.300
## 115    284.1008466 2.736183e+03  7.800 10.400 21.40        25.8     9.600
## 117    284.1008466 1.268332e+03  2.300  4.600 22.60        28.6     9.000
## 119    284.1008466 4.108063e+03 10.250  9.650 21.95        23.6    10.250
## 129    533.2112715 3.044469e+03 13.500 11.900 19.30        17.2     7.300
## 130    227.5673735 2.759938e+03  4.900  6.100 14.60        23.3     8.100
## 134    118.5559924 6.922987e+02  3.800  4.200 17.30        29.0     8.700
## 137     35.3894436 1.387108e+02  6.100  7.800 26.50        26.9    11.600
## 139    172.4698659 1.110865e+01 22.000 14.900 23.20        23.2     7.900
## 140    172.4698659 6.370455e+02  3.600  5.200 23.30        28.1    10.200
## 144    276.7216332 1.322282e+03  3.400  3.800 19.60        24.3     7.500
## 148   1514.5232760 4.017986e+02 23.700 22.000 23.20        14.6     4.400
## 151      4.8159332 9.296169e+00  0.900  5.800 20.70        26.2     5.600
## 153     44.5638347 9.089552e+02  1.700  5.000 14.90        21.7     7.700
## 154     17.0172758 1.140435e+03  5.000 10.100 26.90        24.1    10.300
## 158    566.4835822 3.737311e+03 12.900 14.400 31.60        17.6     6.000
## 167    550.8701088 2.080966e+03  6.700  1.900  7.10         4.9     1.800
## 172    106.9097716 6.691074e+01  3.000 11.500 42.00        21.6     6.900
## 173    106.9097716 1.696737e+02  0.000  0.000  0.00       100.0     0.000
## 175    487.7196735 5.686801e+02  1.600  5.000 30.00        20.4     8.000
## 177    487.7196735 1.518935e+03  7.400 15.100 34.90        20.4     5.500
## 180   3805.6112180 1.700077e+03  2.200  4.900 16.50        14.0     2.900
## 185    206.5630251 7.529816e+02  4.100  9.400 29.80        24.0     9.800
## 193    465.2033757 1.412277e+03  1.200  1.200 11.70        13.9     7.800
## 196    159.5048462 1.136995e+03  6.100 12.100 24.60        21.5     7.000
## 197    507.9153599 4.212013e+03  7.500  8.200 26.80        20.9    10.500
## 200    489.7519680 1.058394e+03  1.700  3.400 19.90        18.8     8.000
## 202    258.7654198 7.273668e+01 26.400 18.200 28.70        16.6     0.800
## 209    263.5621650 1.239154e+03  4.500  7.300 27.80        19.8     8.600
## 213    240.0509263 1.575058e+02  6.700 19.800 40.70        18.0     4.500
## 217    782.4150643 8.937393e+02  2.000  4.800 21.60        22.9     7.100
## 219    998.3536694 9.820147e+02  2.700  6.400 33.70        23.0     9.900
## 220    998.3536694 1.206792e+03 12.400  6.800 16.30        16.0     4.300
## 230    338.8169052 7.494223e+02  8.600 24.600 27.70        19.4     4.300
## 232    338.8169052 7.759940e+02 10.600 18.000 36.90        24.6     5.000
## 233     51.6015557 5.966352e+01  7.100 10.600 43.50        20.2     4.200
## 236     59.4714847 4.538844e+02 15.000 29.700 35.00        15.4     2.200
## 239    143.9259905 3.479869e+02  1.800  5.300 23.60        25.1     7.600
## 240    143.9259905 1.746682e+03  2.700  6.000 27.00        31.0     7.900
## 242      4.6161204 4.823496e+00  2.200 10.400 42.50        26.0     6.400
## 244      0.6714545 3.195858e+00 11.500  0.000  5.40        33.8    17.600
## 245      1.8742292 5.057176e+00  4.100 12.600 39.30        29.1    13.600
## 246     30.2953063 1.153763e+03  2.600  5.600 32.50        19.9     9.500
## 247     77.9288202 2.183669e+03  2.300  6.300 19.00        15.8     5.400
## 253   2121.6753070 3.152299e+03  8.400  9.100 29.60        24.9     8.300
## 257   2121.6753070 9.280679e+02 21.500 13.300 30.10        16.9     5.600
## 261   1080.9999200 1.256028e+03  1.400  1.900  9.90        14.8     5.300
## 264    382.5469159 1.186068e+03  9.600 10.000 27.60        23.1     7.300
## 266    612.1852832 5.548229e+02  1.400  5.500 32.20        30.4     9.400
## 268    197.6435285 7.115083e+02  1.500  3.600 19.10        22.6     7.400
## 273    145.2949266 3.004904e+02  3.600  8.300 31.10        27.8     8.000
## 282     64.7439800 2.171732e+01  3.400  6.100 41.30        31.6     6.100
## 283    222.0709998 1.649494e+03  8.400 17.000 40.60        19.2     6.800
## 287     37.8530224 6.552287e+01  5.600  8.000 37.70        16.6     8.700
## 288     37.8530224 6.552287e+01  5.600  8.000 37.70        16.6     8.700
## 290    164.6866215 7.286557e+02  6.600 16.800 36.20        20.3     6.000
## 300    383.8145872 6.830009e+02  6.100 12.900 41.40        25.6     5.200
## 301    383.8145872 1.415763e+03  6.500 11.800 40.70        21.0     7.100
## 304    112.4656913 1.165953e+03  8.300 15.400 46.40        16.2     6.600
## 311    225.1011703 1.727065e+03  3.200  8.900 35.30        22.8     5.500
## 312    225.1011703 1.727065e+03  2.100  3.900 32.20        20.7     9.000
## 314    133.4732566 1.110615e+03  4.300 14.100 37.50        19.4     6.600
## 315    297.1780980 3.057872e+02  1.300 23.100 35.10        17.4     0.000
## 316    297.1780980 8.576169e+02  5.200 14.200 40.40        19.2     7.100
## 317    297.1780980 1.649394e+03  5.600 10.700 33.40        25.2     7.100
## 320     89.4608365 8.185634e+01  5.200  8.000 35.70        22.9    10.000
## 322     27.2893762 9.857699e+01  3.200  3.100 39.30        22.5    12.900
## 323     11.8713070 6.448261e+00  1.500  5.500 53.60         5.8    24.500
## 325     26.7553698 9.917301e+01  5.200 10.000 41.30        21.3     8.000
## 333     37.8504274 7.818290e+02  4.200  6.700 38.60        30.1    11.800
## 336    139.2598121 4.388037e+02  9.900 12.900 36.10        26.7     7.700
## 337      6.0290014 6.738057e+00  4.600  6.600 36.10        24.9    10.300
## 339      8.8000506 9.915191e+00  0.000  0.000 64.30        21.4    14.300
## 342      6.2758149 7.722580e+00  3.600  2.100 45.50        36.1     9.400
## 351    119.6533117 7.502819e+02  5.700  9.500 33.70        24.5     7.600
## 355     12.8461480 1.492575e+01  6.700 10.200 37.00        23.0     7.500
## 356     81.4211806 3.135693e+02  4.600  8.100 37.20        21.4     8.000
## 359     91.5973753 8.679930e+01  6.200  8.300 32.90        20.8     4.300
## 360     65.3807673 1.173069e+02  4.700  6.900 32.70        22.5     8.900
## 366    384.8257603 1.400095e+03  6.000 12.800 26.10        21.2     4.800
## 368     73.2096452 7.892232e+01  7.600  7.600 27.50        19.7     7.300
## 369     15.6748796 2.150233e+01  7.200 19.700 44.10        22.1     4.800
## 370     31.9075499 4.475296e+01 11.900 12.300 35.50        16.9     4.600
## 373     69.9736832 1.722875e+01  8.700 19.200 39.00        18.1     6.000
## 374     69.9736832 8.072789e+02  9.100 14.200 36.10        20.3     5.000
## 376    373.2122172 3.085429e+02  9.200 22.500 30.10        19.6     2.800
## 377     20.8377484 5.327990e+01  3.600 13.100 42.20        16.7     4.300
## 385     36.7133483 8.322532e+02  4.400 13.200 43.10        23.5     4.200
## 386     59.0892400 2.252477e+02  0.000 16.300 54.70         9.5     3.600
## 391    519.5093907 3.954676e+02  1.800  2.500 18.00        16.8     6.100
## 392    519.5093907 1.102286e+03  5.800  7.900 32.10        20.1     7.100
## 393    112.7376864 1.815593e+02  0.000 16.500 64.80        18.7     0.000
## 396    690.6456182 3.270998e+03  7.700 14.400 32.60        22.7     6.900
## 401   2961.9891250 3.409478e+03  6.600 16.600 32.80        21.0     4.600
## 406    382.7440202 3.514398e+03 21.600 16.200 29.70        14.4     8.000
## 407    582.5352975 1.554721e+03 13.400  9.100 38.40        17.5     8.800
## 411    289.9737799 2.079717e+03 15.400 10.300 23.40        21.7     1.100
## 412    289.9737799 2.079717e+03 15.400 10.300 23.40        21.7     1.100
## 415   4793.7080190 1.320084e+04  1.400  0.800  9.00         8.5     1.800
## 416   4793.7080190 4.707373e+03  5.500  4.700 17.50        10.4     2.900
## 422     94.0773175 3.777545e+02  4.200 11.100 34.30        23.1     8.700
## 423    106.6422934 9.529861e+01  4.200  9.200 37.30        25.3     9.000
## 425      9.5434181 5.027406e+01  2.300  9.600 32.80        26.4     6.800
## 435     10.1522317 2.662313e+00  0.000 11.500 48.80        22.0     8.800
## 436    106.8370287 8.271917e+01  2.900 12.600 45.20        21.5     5.600
## 437    133.1651687 6.110224e+02  3.900  9.500 18.30        35.8     4.200
## 438    535.0400447 2.197567e+03  3.100  8.200 21.50        27.9     9.900
## 443   1148.4304360 1.843374e+03 27.400 25.400 29.00        11.8     2.800
## 446   1148.4304360 9.937758e+02  1.300  4.100 17.20        17.6     6.400
## 447   1148.4304360 1.002475e+03 16.900 12.500 19.70        14.3     5.600
## 451      5.4561216 3.960187e+00  2.400 13.800 29.70        38.6     6.900
## 452    273.7293946 1.127257e+03  1.100  3.100 19.20        22.0    10.100
## 453    803.7592150 1.957523e+03  6.800  7.400 23.30        22.6     7.600
## 458     85.2446210 2.090478e+02  3.900  5.900 31.30        21.9    12.400
## 464     12.3743778 1.102200e+03  2.700  7.000 30.70        28.4     9.200
## 467    239.2640025 6.489028e+02  1.200  5.200 40.30        23.9    10.200
## 472     20.0374771 2.966812e+01  8.300 14.300 31.00        22.3     6.300
## 473    125.8578542 7.766601e+02  6.600  8.100 22.90        25.8     8.100
## 477     44.0413044 7.526151e+01  6.300 17.700 32.60        24.4     8.500
## 483    215.6845729 1.622551e+02  2.800  4.800 28.00        23.5     7.700
## 490   1991.3164500 1.915718e+03  7.800 19.900 31.10        22.9     4.400
## 492   1991.3164500 5.992744e+02  2.200 11.700 18.80        16.7    14.100
## 493     11.6377665 1.711518e+03  3.500  8.800 30.30        27.4     7.600
## 494      6.9005193 3.716512e+01  2.200  6.300 37.90        22.1     8.400
## 496      6.9005193 4.243751e+01  2.100  6.600 32.90        24.6     8.900
## 503     16.2721512 4.382716e+00  3.600  6.100 28.30        22.2    13.000
## 506      1.5962854 1.574446e+00  4.600  8.400 43.00        22.6     6.000
## 507     18.3787182 1.852130e+01  3.300  6.400 37.30        23.9     6.900
## 509    607.8688394 2.446117e+03 12.000 11.100 27.30        23.2     4.300
## 514     19.3050871 6.077509e+01  4.300 11.800 30.40        22.8     9.600
## 515     20.0339410 3.576645e+01  1.300  5.100 32.30        24.0     7.900
## 516     95.4692804 3.322028e+03 21.900 20.500 30.90        16.7     3.400
## 517     95.4692804 7.582569e+00  0.000 21.300 32.00        42.2     4.400
## 524     60.5307259 1.024548e+02  2.400  7.400 35.40        25.5     8.800
## 525     76.8261839 2.655947e+02  0.400  0.500 12.50         6.2     7.500
## 527    190.7560141 2.606413e+02  4.100  6.400 34.10        20.9     7.200
## 528    190.7560141 1.434396e+03 11.500 17.600 34.40        15.1     5.800
## 532   1499.8024730 8.333857e+02  8.100  9.900 46.60        13.5     2.500
## 533    896.3284316 2.971920e+03 13.200 24.000 37.90        16.2     2.400
## 535   2398.2785010 6.867870e+03  7.300 17.400 39.10        20.2     5.700
## 536    345.6733525 2.551158e+02  2.300  5.700 49.10        16.9     6.300
## 549    117.5795993 2.677302e+02  4.400 11.800 42.90        16.0     6.400
## 550    220.3749435 1.543258e+03  2.800  3.700 24.50        25.6     8.800
## 553     21.2173544 4.259276e+02  6.500  6.200 12.90        22.7     4.600
## 555      2.8764507 4.425293e+01  5.500  6.900 26.30        27.5     4.400
## 556      5.6915564 4.285971e+01  8.600  8.100 30.80        21.7    14.400
## 558      9.1075031 1.370960e+02  6.300 12.700 30.90        24.4     9.300
## 559     29.1525842 1.729465e+02  5.100  5.900 19.60        19.6     5.700
## 566    340.3141664 1.653110e+03  3.800 15.600 39.30        20.5    10.700
## 568      8.4720787 7.332968e+00  0.400  5.500 32.70        21.6     9.000
## 575    231.6574260 9.287181e+02  1.300  3.300 21.20        17.6     6.600
## 579   3100.5067700 2.407329e+03  3.700  6.900 33.60        18.5     9.200
## 581     27.4855283 1.945556e+01  6.900  9.900 38.30        19.7    14.200
## 583    851.2357955 1.782710e+03  0.600  1.900  8.10         7.8     2.700
## 589    189.0697387 9.136056e+02  3.500  6.500 29.00        28.3    11.700
## 603     20.5140465 1.191247e+01  7.800  9.400 40.50        25.4     8.800
## 604    677.8190839 1.434718e+03 10.600 11.100 22.10        20.4     5.700
## 610     99.5779870 3.575044e+02  8.400 12.400 28.90        23.0     7.600
## 611     99.5779870 1.154858e+02  8.400 12.400 28.90        23.0     7.600
## 614     10.2237354 2.457600e+01  4.900 10.100 29.70        20.4    13.700
## 616    416.5081331 6.727994e+02  5.100  5.500 14.30        17.2     5.900
## 617     63.0982122 1.289339e+02  4.200  5.400 16.40        20.7     8.300
## 619      0.2631477 9.188156e-01  7.000  6.900 39.60        17.8    10.500
## 621     32.7658189 3.688392e+02  2.500  3.600 21.80        23.9     9.100
## 622      3.1185601 5.339576e+00 11.800  3.600 26.00        16.2    20.500
## 625    304.3230514 7.721269e+02  3.500  7.700 33.40        23.2     8.100
## 626    134.3756043 7.347544e+02  5.200 18.400 33.70        23.8     8.500
## 628   1081.0755160 1.937322e+03  7.600 17.400 21.60        17.3     5.800
## 630   1081.0755160 1.937322e+03  7.600 17.400 21.60        17.3     5.800
## 631   1081.0755160 1.138168e+03  9.300 22.700 35.60        18.5     5.000
## 633   1081.0755160 1.766753e+03  9.300 22.700 35.60        18.5     5.000
## 636    844.0560682 7.475024e+02  3.700 11.600 28.70        19.1     3.500
## 640    763.2187561 1.225476e+03 10.900 16.700 33.10        21.5     5.900
## 650    236.9250210 3.887089e+02  1.800  7.900 41.50        25.4     9.500
## 652    500.4640531 1.553084e+03  7.000 18.900 41.50        21.1     6.100
## 653    500.4640531 1.252522e+03  2.500  5.700 29.80        23.4     9.400
## 655    224.0157960 8.769978e+02 12.100 16.000 34.30        18.5     8.400
## 657    447.6704633 1.049876e+03  6.000 17.400 32.50        21.1     6.300
## 662    252.0806270 7.569190e+02  9.700 17.400 29.70        37.4     0.600
## 664    506.8050307 7.892833e+02  2.400 11.900 20.70        25.9    10.800
## 669     33.8199501 5.575203e+01  5.100 14.500 33.10        23.6     6.700
## 672     26.1173068 1.861925e+00 12.600 24.500 46.40         9.3     4.600
## 674     24.3100485 1.371803e+01  9.100 17.600 37.30        21.3     2.100
## 677     20.1780332 3.355024e+01  2.000  3.000 21.10        28.7    11.300
## 680     28.1864282 4.875937e+01 11.400 12.400 33.40        26.4     7.100
## 684     29.8252511 1.285163e+03  3.300  5.800 24.80        32.9     9.100
## 686     29.8252511 1.141449e+03  3.900 11.300 28.80        29.6     8.300
## 689    658.2795860 2.815162e+03  4.600  7.600 23.60        25.7     7.800
## 690    658.2795860 9.392533e+02  3.700  6.000 19.80        20.2     5.100
## 691      9.1123692 1.691982e+01  3.400  8.400 27.30        27.5    12.600
## 692      4.8813373 2.262715e+01  3.000  7.600 32.40        24.6     8.600
## 693    282.3994922 4.333113e+02  4.400  5.500 19.20        22.7     9.000
## 694     75.4885553 3.054594e+01  8.600  9.900 44.20        12.5     6.400
## 695    646.9713784 3.889874e+03  2.900  8.400 33.40        20.6     6.400
## 698    646.9713784 3.613702e+02  5.300  4.700 46.80        13.3    14.000
## 702    185.4727921 4.376480e+02  7.300 10.700 42.10        14.7     8.100
## 703    399.4821765 1.196322e+03  3.100 13.500 49.70        20.3     3.300
## 704     80.5908680 5.302185e+02  9.200 11.200 51.10         8.7     8.000
## 705     53.5676469 3.772888e+02  0.000  0.000  0.00        79.4     0.000
## 709   1173.9499840 2.370235e+03  7.600 15.800 45.30        16.7     5.700
## 710    135.5522610 5.863915e+02 10.100 18.500 44.60        10.6     5.700
## 711    180.3497596 8.184597e+02  3.400  6.800 43.30        18.4    11.500
## 714    639.3534244 2.672717e+03  1.600  5.000 23.10        16.1     6.400
## 715    310.9685288 5.707147e+02  4.100  6.600 27.00        18.2    10.200
## 718   4393.6457430 9.938713e+03  4.550 11.075 45.00        16.3     5.950
## 720   4393.6457430 4.098322e+03  4.400 13.200 22.40        15.6     4.900
## 722     93.6298585 1.562325e+02  4.000  8.700 42.80        15.8     8.000
## 723     93.6298585 3.101584e+01  3.600 10.800 47.60        16.7     7.200
## 725    185.7410663 7.372225e+02 10.800 18.800 47.00         9.8     4.900
## 728    590.8582870 3.232986e+03 14.700 14.400 30.30        17.3     5.700
## 730    590.8582870 1.229869e+03  3.800  7.400 28.10        19.6     5.400
## 734     20.8210161 2.328907e+01  9.300 11.800 37.30        19.2     7.700
## 735     66.0674464 3.107408e+02  4.700  8.300 28.60        19.8     8.300
## 741    196.0957023 0.000000e+00 39.400  0.000 21.20        18.2     0.000
## 749      0.6278594 4.139258e-01  0.000 33.000 30.40        25.4     1.300
## 752     14.0376351 4.360830e+01  3.500  7.500 32.00        26.5     8.600
## 753     14.0376351 2.369572e+02  3.500  7.500 32.00        26.5     8.600
## 756    239.4941639 1.310463e+03  5.400 14.000 23.00        20.1     1.300
## 759     40.3834167 1.472121e+02  8.000  9.100 34.30        32.0     2.900
## 762   1049.4266430 2.514901e+03 10.275 12.825 30.05        25.3     7.775
## 765     58.9806697 1.155230e+03 17.000 15.000 28.30        22.5     5.700
## 768    305.2569002 1.550880e+03 48.000 18.900 18.10        10.9     1.800
## 769    305.2569002 1.250256e+03 48.000 18.900 18.10        10.9     1.800
## 770    927.5773904 1.054116e+03 30.600 19.900 28.30        16.1     1.700
## 771    927.5773904 5.884356e+02 15.000 14.900 29.30        23.2     7.400
## 785     37.3422486 8.839382e+01  4.900  6.300 18.90        26.7     6.900
## 797    154.9786308 6.283662e+02  0.900  2.700 23.40        26.6     9.700
## 800    112.6440858 1.837190e+03  4.000  6.100 18.90        17.2     6.400
## 805    288.4485648 8.413824e+02  8.500 14.900 31.00        23.4     5.600
## 807   1068.2611400 3.864172e+03 12.700  6.600 16.50        12.8     4.800
## 809     73.1173460 5.135142e+01  5.200  8.300 36.00        15.9    11.700
## 814     34.7020380 1.121811e+02 11.100 12.100 29.00        16.5     4.400
## 815    529.1733396 6.378911e+02  7.800 12.800 28.60        22.3     7.800
## 818   1732.1877740 2.413394e+03  0.000  0.000 44.70        37.5    17.800
## 820    880.2351104 5.488993e+02 10.700 14.100 31.50        19.8     2.800
## 830    125.2400856 9.627495e+02  4.400 11.500 42.70        18.1     4.700
## 837     82.6786703 7.796840e+02  0.800  4.100 25.40        24.6     5.700
## 838     70.5559328 8.021284e+02  3.700  9.200 37.20        20.3     5.800
## 843     91.6669646 3.804301e+02  4.800  4.900 34.40        22.5     7.800
## 845    180.7712563 1.237443e+03 10.600  9.600 34.60        21.9     7.400
## 851     97.9927046 2.587213e+02  2.300  6.400 37.90        23.5    10.900
## 855   1515.8208580 4.980709e+03  0.000  3.900 11.20        10.7     3.900
## 856   1515.8208580 1.580861e+03  4.700  8.000 35.60        23.9     7.700
## 857   1515.8208580 8.107966e+02  0.000  3.900 11.20        10.7     3.900
## 859    143.1170929 3.639882e+01  3.700  3.700 28.00        23.7    12.500
## 864    273.9173936 1.031774e+03  3.100  6.400 25.40        23.8     9.100
## 870     13.1874175 2.323895e+02  0.000  0.000 71.90        28.1     0.000
## 874      0.8096509 4.475036e+00  0.600  4.500 25.80        29.7    11.100
##     bachelor   grad      pov hs_orless urc2013 urc2006        aod
## 3     12.700  5.100 19.00000    53.700       4       4  36.000000
## 5     10.000  5.400  8.80000    45.400       4       4  43.416667
## 6     13.700  9.800 15.60000    47.200       4       4  33.000000
## 7      5.900  2.000 25.50000    61.400       1       1  39.583333
## 8     17.600  8.700  7.30000    40.000       1       1  38.750000
## 9      7.100  2.900  8.10000    68.700       1       1  40.363636
## 14     2.200  0.400 13.30000    70.600       2       2  42.636364
## 16     7.800  4.200 23.20000    59.100       3       3  42.000000
## 18     7.600  3.500 23.00000    64.100       3       3  39.500000
## 20     9.500  5.900 37.70000    60.900       3       3  31.250000
## 24    10.300  3.500 19.30000    57.600       2       2  35.833333
## 26     0.000  0.000 15.60000    89.500       4       5  12.833333
## 27    13.600 11.400 64.30000    24.000       4       4  29.250000
## 28     4.200  2.000 29.50000    68.600       1       1  46.333333
## 33     2.700  0.600 35.90000    70.800       4       5   8.833333
## 37    12.300  5.400  7.10000    41.800       2       2  29.000000
## 42     8.100  4.500 15.30000    60.200       6       6  63.125000
## 44    16.300  5.700  9.90000    44.500       2       2  43.300000
## 46    14.000  7.300 16.60000    49.100       4       4  33.333333
## 47     5.400  2.800 23.40000    69.500       6       6  51.000000
## 48     5.500  3.900 32.90000    53.900       5       5  37.571429
## 50    13.900 10.300 23.60000    49.100       5       5  32.166667
## 52    21.700 15.600 23.70000    37.500       3       3  49.125000
## 56     9.300  4.600 21.00000    65.200       3       3  36.166667
## 62    11.100  8.700 10.10000    43.500       6       6  32.363636
## 65     5.400  1.500 31.30000    63.100       3       3  83.363636
## 68    14.900  7.400 10.90000    41.100       5       5  17.000000
## 69    16.900  7.700 12.60000    39.900       5       5  39.571429
## 72    10.800  5.100 22.30000    52.500       4       4  53.111111
## 73     0.000 75.000  0.00000    25.000       6       5   5.000000
## 78     4.900  2.500 22.10000    63.300       3       3  55.875000
## 80    15.400  6.300  9.80000    42.000       5       5  26.833333
## 81    15.400  7.800  5.70000    47.200       1       1  32.909091
## 82    20.100  6.900 10.30000    41.800       1       1  55.090909
## 89    25.300 13.800  6.90000    29.800       1       1  96.600000
## 90    10.000  3.800 21.80000    48.500       1       1  24.083333
## 92    13.300  8.100 14.40000    42.400       3       4  45.500000
## 93    11.000  3.600 12.70000    56.200       3       3  38.250000
## 94    19.000  9.200 11.30000    32.600       5       5  37.181818
## 96    12.600  4.500 13.30000    58.300       1       1  82.333333
## 99    13.900  7.300 14.80000    28.500       6       6  45.166667
## 109   13.200  4.200  9.40000    50.200       2       2  21.800000
## 110    9.700  4.300 12.20000    57.100       2       2  50.272727
## 111    8.700  4.200 20.90000    52.400       2       2  26.583333
## 114    5.900  2.100 41.60000    74.200       2       2  27.181818
## 115   16.600  8.400 10.00000    39.600       1       1  77.000000
## 117   21.800 11.100  6.80000    29.500       1       1  53.000000
## 119   16.350  7.975 12.12500    41.850       1       1  74.200000
## 129   19.500 11.300 15.90000    44.700       1       1  86.375000
## 130   27.600 15.400  5.40000    25.600       3       3  38.909091
## 134   22.700 14.300  5.80000    25.300       3       3  44.181818
## 137   14.300  6.900 11.30000    40.400       3       3  60.300000
## 139    5.600  3.200 17.00000    60.100       3       3  15.363636
## 140   21.600  8.000  4.40000    32.100       3       3  26.250000
## 144   27.500 13.900  8.20000    26.800       2       2  59.666667
## 148    9.300  2.900 32.00000    68.900       1       1  53.100000
## 151   25.700 15.200  4.20000    27.400       2       2  26.333333
## 153   29.700 19.300  9.50000    21.600       3       3  29.333333
## 154   15.400  8.200 14.40000    42.000       4       4  37.333333
## 158   10.900  6.500 22.10000    58.900       3       3  53.400000
## 167   26.800 50.700  6.30000    15.700       3       3  37.000000
## 172    9.500  5.600 11.80000    56.500       4       4  67.000000
## 173    0.000  0.000  0.82500     0.000       4       4  64.090909
## 175   22.400 12.700  3.50000    36.600       2       2  52.000000
## 177   10.200  6.400 31.80000    57.400       2       2  47.500000
## 180   26.800 32.700 18.90000    23.600       1       1  59.500000
## 185   14.300  8.600 12.30000    43.300       3       3  31.000000
## 193   37.600 26.500  1.10000    14.100       1       1  22.000000
## 196   20.400  8.400 38.90000    42.800       3       3  46.083333
## 197   18.400  7.700 11.40000    42.500       1       1  55.000000
## 200   30.600 17.500  5.50000    25.000       1       1  43.695334
## 202    7.600  1.700 42.30000    73.300       2       2  41.500000
## 209   19.600 12.300 12.50000    39.600       3       3  43.695334
## 213    7.700  2.700 24.90000    67.200       3       3  48.714286
## 217   29.300 12.300  6.40000    28.400       2       2  42.750000
## 219   15.400  8.800 15.00000    42.800       2       2  49.833333
## 220   27.900 16.200 11.00000    35.500       2       2  48.666667
## 230    9.500  5.900 37.70000    60.900       3       3  33.000000
## 232    3.300  1.600 37.80000    65.500       3       3  33.000000
## 233    9.200  5.200 14.50000    61.200       5       5  36.500000
## 236    2.500  0.100 48.30000    79.700       3       3  28.571429
## 239   27.500  9.000  6.60000    30.700       3       3  49.555556
## 240   16.500  8.900 13.10000    35.700       3       3  40.250000
## 242    8.600  3.900 10.00000    55.100       6       6  27.600000
## 244   24.500  7.200 12.50000    16.900       6       6  23.500000
## 245    1.200  0.000 25.80000    56.000       6       6  27.200000
## 246   19.700 10.100  4.50000    40.700       5       5  41.500000
## 247   23.800 27.400 20.70000    27.600       4       4  38.700000
## 253   13.600  6.000  9.20000    47.100       1       1 103.000000
## 257    8.100  4.500 16.20000    64.900       1       1 101.500000
## 261   36.300 30.300  2.20000    13.200       2       2  62.777778
## 264   14.900  7.500  9.40000    47.200       2       2  51.888889
## 266   14.600  6.600  2.50000    39.100       2       2  60.000000
## 268   30.800 15.100  2.90000    24.200       2       2  54.500000
## 273   13.800  7.400 13.30000    43.000       2       2  39.000000
## 282    6.600  4.900 12.60000    50.800       2       2  34.818182
## 283    4.700  3.300 32.40000    66.000       3       3  45.333333
## 287   15.700  7.600  5.60000    51.300       5       5  40.250000
## 288   15.700  7.600  5.60000    51.300       5       5  40.833333
## 290    9.800  4.400 18.80000    59.600       4       4  46.375000
## 300    6.100  2.800 40.60000    60.400       2       2  46.000000
## 301    9.000  3.900 11.80000    59.000       2       2  67.000000
## 304    5.400  1.700 33.00000    70.100       2       4  48.181818
## 311   13.000 11.300 16.50000    47.400       3       3  41.666667
## 312   18.300 13.700  6.20000    38.200       3       3  41.666667
## 314   11.800  6.200 20.30000    55.900       4       4  36.090909
## 315    9.000 14.000  0.00000    59.500       3       3  43.916667
## 316    9.500  4.400 14.10000    59.800       3       3  45.909091
## 317   12.600  5.400 15.00000    49.700       3       3  43.916667
## 320   14.300  3.800 11.00000    48.900       4       4  34.111111
## 322   12.400  6.600  3.10000    45.600       5       5  46.666667
## 323    8.500  0.600  0.00000    60.600       6       6  39.125000
## 325    9.600  4.600 16.90000    56.500       5       5  33.700000
## 333    6.500  2.100  9.80000    49.500       3       3  38.600000
## 336    4.900  1.900 17.70000    58.900       3       3  42.000000
## 337   12.600  4.800 10.40000    47.300       6       6  36.181818
## 339    0.000  0.000  0.00000    64.300       6       6  20.500000
## 342    1.300  2.100 13.70000    51.200       2       2  28.750000
## 351    9.100 10.000 15.60000    48.900       3       3  31.272727
## 355    9.300  6.200 17.40000    53.900       3       4  31.666667
## 356   12.400  8.300 11.80000    49.900       4       4  48.272727
## 359   16.900 10.600 12.00000    47.400       5       5  29.916667
## 360   13.700 10.600 10.30000    44.300       4       4  32.750000
## 366   19.500  9.700 21.70000    44.900       2       2  66.900000
## 368   16.600 13.800 13.10000    42.700       5       5  34.333333
## 369    2.100  0.000 19.50000    71.000       6       6  30.583333
## 370    9.000  9.800 18.50000    59.700       6       6  32.090909
## 373    6.600  2.300 15.20000    66.900       4       4  35.500000
## 374   11.100  4.100 21.80000    59.400       4       4  40.181818
## 376   10.400  5.400 33.20000    61.800       3       3  40.000000
## 377   12.200  7.900 11.10000    58.900       3       3  40.000000
## 385    8.800  2.800 14.10000    60.700       2       2  43.695334
## 386   14.100  1.800 19.20000    71.000       4       5  32.916667
## 391   29.000 25.800  1.50000    22.300       2       2  44.000000
## 392   18.300  8.600  5.30000    45.800       2       2  45.416667
## 393    0.000  0.000  0.00000    81.300       2       2  49.333333
## 396    9.700  6.000 12.00000    54.700       2       2  58.333333
## 401   11.100  7.300 21.20000    56.000       1       1  53.416667
## 406    7.000  3.100 21.40000    67.500       2       2  29.600000
## 407    8.700  4.000 17.40000    60.900       2       2  36.714286
## 411   15.600 12.600 28.60000    49.100       3       3  29.625000
## 412   15.600 12.600 28.60000    49.100       3       3  29.625000
## 415   36.400 42.100  6.40000    11.200       1       1  52.000000
## 416   35.100 24.100 18.20000    27.700       1       1  52.000000
## 422   12.100  6.500 12.60000    49.600       4       4  56.800000
## 423   10.300  4.800 10.10000    50.700       4       4  42.750000
## 425   13.900  8.200 11.00000    44.700       5       5  38.000000
## 435    5.700  3.100 11.50000    60.300       5       5  27.500000
## 436    8.700  3.400  7.20000    60.700       4       4  34.500000
## 437   21.600  6.700 28.20000    31.700       4       4  26.250000
## 438   18.600 10.800 15.10000    32.800       2       2  74.428571
## 443    3.000  0.700 34.30000    81.800       1       1  95.000000
## 446   30.600 22.900  2.90000    22.600       2       2 116.000000
## 447   15.300 15.700 25.40000    49.100       1       1  95.000000
## 451    6.500  2.000 10.10000    45.900       5       5  40.000000
## 452   30.900 13.600  3.60000    23.400       2       2  67.400000
## 453   22.500  9.800  8.50000    37.500       1       1  43.695334
## 458   16.200  8.400  7.80000    41.100       4       4  35.444444
## 464   15.200  6.700 26.90000    40.400       3       3  29.666667
## 467   12.000  7.300  4.30000    46.700       2       2  24.000000
## 472   12.900  4.900 19.00000    53.600       5       5  33.666667
## 473   19.100  9.400 11.50000    37.600       3       3  38.090909
## 477    6.800  3.700 27.30000    56.600       5       5  32.666667
## 483   22.200 11.000  6.30000    35.600       2       2  36.272727
## 490    9.000  4.800 29.10000    58.800       1       1  73.833333
## 492   11.800 24.800  0.00000    32.700       1       1  73.833333
## 493   16.400  6.000 13.40000    42.600       4       4  28.200000
## 494   17.100  6.100  8.90000    46.400       5       5  29.000000
## 496   17.500  7.400  9.30000    41.600       5       5  29.333333
## 503   13.300 13.500 11.90000    38.000       4       4  24.200000
## 506   12.200  3.300 12.40000    56.000       6       6  22.500000
## 507   15.100  7.300 11.40000    47.000       5       5  22.833333
## 509   14.700  7.400 19.80000    50.400       3       3  42.000000
## 514   15.300  5.800 12.30000    46.500       5       5  27.777778
## 515   22.900  6.500  2.70000    38.700       3       3  31.600000
## 516    5.000  1.700 27.70000    73.300       1       1  20.500000
## 517    0.000  0.000  5.15000    53.300       1       1  15.416667
## 524   12.900  7.600  5.40000    45.200       5       5  30.666667
## 525   35.300 37.600  4.40000    13.400       2       2  58.166667
## 527   19.500  7.700  4.50000    44.600       3       3  92.500000
## 528   11.100  4.600 28.10000    63.500       3       3  95.800000
## 532   16.500  2.900  3.20000    64.600       2       2  70.888889
## 533    5.400  0.900 41.30000    75.100       2       2  75.375000
## 535    8.300  1.900 32.60000    63.800       1       1  63.111111
## 536   14.900  4.800  8.80000    57.100       2       2  58.000000
## 549   12.700  5.700 10.20000    59.100       3       3  46.444444
## 550   19.700 14.800  8.90000    31.000       3       3  12.090909
## 553   26.700 20.400  6.80000    25.600       3       3  11.909091
## 555   23.300  6.100 10.20000    38.700       5       5  23.083333
## 556   14.200  2.200  6.60000    47.500       5       5  15.416667
## 558   10.000  6.400 14.40000    49.900       4       4   7.800000
## 559   22.700 21.400  9.60000    30.600       4       4  19.444444
## 566    6.700  3.400 16.10000    58.700       1       1  71.400000
## 568   17.600 13.100 10.60000    38.600       6       6  25.166667
## 575   21.800 28.100  7.90000    25.800       3       3  48.142857
## 579   17.400 10.700  5.50000    44.200       1       1  43.695334
## 581    6.100  4.900 10.20000    55.100       5       5  35.125000
## 583   35.900 42.900  2.10000    10.600       2       2  58.285714
## 589   14.100  6.900 14.10000    39.000       3       3  57.500000
## 603    3.700  4.300 16.00000    57.700       6       6  52.666667
## 604   20.600  9.500 20.50000    43.800       1       1  45.750000
## 610   12.700  7.100 23.30000    49.700       4       4  48.833333
## 611   12.700  7.100 23.30000    49.700       4       4  46.363636
## 614   12.300  8.900 10.70000    44.700       6       6  19.500000
## 616   31.700 20.300 12.10000    24.900       1       3  56.181818
## 617   25.000 20.100 11.60000    26.000       5       5  16.583333
## 619   13.600  4.600  9.50000    53.500       5       5  35.200000
## 621   26.200 13.000  7.90000    27.900       4       4  27.285714
## 622   18.300  3.500  7.10000    41.400       6       6  23.375000
## 625   16.200  7.900  6.90000    44.600       2       2  51.636364
## 626    7.100  3.300 22.40000    57.300       4       4  36.818182
## 628   17.000 13.300 35.70000    46.600       1       1  80.000000
## 630   17.000 13.300 35.70000    46.600       1       1 131.000000
## 631    4.300  4.500 35.90000    67.600       1       1 131.000000
## 633    4.300  4.500 35.90000    67.600       1       1 131.000000
## 636   21.400 12.000 24.10000    44.000       1       1  60.090909
## 640    8.700  3.100 19.10000    60.700       1       1  50.800000
## 650    9.000  5.000  8.60000    51.200       2       2  39.333333
## 652    4.300  1.200 36.20000    67.400       3       3  58.000000
## 653   18.900 10.200  7.50000    38.000       3       3  61.428571
## 655    7.400  3.300  0.00000    62.400       3       3  47.700000
## 657    8.400  8.400 38.70000    55.900       3       3  55.090909
## 662    5.200  0.000 15.20000    56.800       3       3  41.111111
## 664   20.200  8.000 27.80000    35.000       3       3  41.000000
## 669   11.700  5.300 23.70000    52.700       5       5  40.416667
## 672    0.000  2.600  0.00000    83.500       5       5  30.583333
## 674    8.500  4.000  8.60000    64.000       3       3  28.900000
## 677   22.900 11.000  4.90000    26.100       4       4  32.750000
## 680    6.000  3.200  7.60000    57.200       4       4  32.625000
## 684   16.200  7.900  7.70000    33.900       3       3  45.571429
## 686   11.700  6.500 17.40000    44.000       3       3  42.714286
## 689   21.200  9.600 12.20000    35.800       1       1  69.000000
## 690   32.600 12.600 13.50000    29.500       1       1  63.666667
## 691   12.000  8.700  6.80000    39.100       5       5  28.666667
## 692   15.600  8.100 11.60000    43.000       5       5  25.800000
## 693   24.000 15.300  6.00000    29.100       2       2  44.285714
## 694   11.200  7.200  7.80000    62.700       4       5  32.272727
## 695   18.400  9.800 15.30000    44.700       1       1  37.600000
## 698   11.600  4.300  8.80000    56.800       1       1  34.545455
## 702   10.400  6.600  7.80000    60.100       3       3  40.888889
## 703    7.500  2.600  5.50000    66.300       2       2  52.900000
## 704   10.100  1.700 31.20000    71.500       4       4  30.800000
## 705    0.000 20.600 10.62500     0.000       4       4  33.444444
## 709    5.800  3.200 27.90000    68.700       2       2  53.909091
## 710    7.100  3.500 32.10000    73.200       3       3  44.166667
## 711   13.200  3.500  5.80000    53.500       3       3  27.500000
## 714   28.600 19.300  3.10000    29.700       2       2  44.916667
## 715   22.000 11.800  2.40000    37.700       3       3  54.111111
## 718   11.675  5.425 16.36667    60.625       1       1  69.666667
## 720   23.900 15.700 12.20000    40.000       1       1  69.666667
## 722   14.400  6.300  8.90000    55.500       2       2  40.454545
## 723   10.000  4.100  7.90000    62.000       2       2  24.777778
## 725    7.100  1.700 38.10000    76.600       3       3  49.555556
## 728   10.400  7.100 22.40000    59.400       1       1  29.100000
## 730   21.100 14.600  2.90000    39.300       1       1  29.100000
## 734   12.500  2.300 14.80000    58.400       3       3  38.500000
## 735   18.300 12.000 11.30000    41.600       4       4  44.090909
## 741   21.200  0.000  3.97500    60.600       3       3  45.083333
## 749    7.600  2.200 40.00000    63.400       6       6  37.700000
## 752   14.900  7.100 14.90000    43.000       4       4  30.750000
## 753   14.900  7.100 14.90000    43.000       4       4  30.750000
## 756   21.200 15.100 19.80000    42.400       3       3  36.000000
## 759    9.800  3.900 20.30000    51.400       4       4  42.125000
## 762    9.550  4.250  5.47500    53.150       1       1  66.500000
## 765    8.500  3.000 16.60000    60.300       4       4  13.083333
## 768    1.500  0.900 59.90000    85.000       3       3  13.363636
## 769    1.500  0.900 59.90000    85.000       3       3  11.909091
## 770    2.700  0.800 23.00000    78.800       1       1  37.444444
## 771    6.900  3.400 20.10000    59.200       1       1  30.500000
## 785   24.800 11.600 14.00000    30.100       4       4  41.428571
## 797   26.100 10.500  3.30000    27.000       3       3  88.333333
## 800   29.100 18.400 15.50000    29.000       4       4  36.800000
## 805   11.900  4.800 12.70000    54.400       2       2  54.833333
## 807   25.300 21.200 12.80000    35.800       2       2  54.833333
## 809   11.800 11.100  2.70000    49.500       4       4  35.500000
## 814   15.700 11.200 11.30000    52.200       4       4  34.750000
## 815   15.100  5.600 22.60000    49.200       3       3  30.666667
## 818    0.000  0.000  4.12500    44.700       2       2 138.000000
## 820   12.900  8.100 34.80000    56.300       3       3  26.181818
## 830   11.400  7.100 18.90000    58.600       3       4  37.000000
## 837   26.100 13.300  7.20000    30.300       4       3  39.000000
## 838   15.100  8.700 11.30000    50.100       5       5  31.000000
## 843   16.000  9.500  5.20000    44.100       4       4  39.181818
## 845   10.700  5.200 18.40000    54.800       3       3  61.500000
## 851   13.400  5.500 12.00000    46.600       4       4  27.714286
## 855   45.800 24.600  0.00000    15.100       1       1  89.571429
## 856   13.900  6.200 10.80000    48.300       1       1 116.400000
## 857   45.800 24.600  0.00000    15.100       1       1  89.571429
## 859   18.000 10.300  2.80000    35.400       2       2  38.285714
## 864   21.800 10.500  8.20000    34.900       2       2  43.375000
## 870    0.000  0.000  5.10000    71.900       4       4  24.666667
## 874   11.700 16.700  1.60000    30.900       6       6  24.714286
##                 id.y     .pred .row   value.y              .config
## 3   train/test split 11.951434    3 11.212174 Preprocessor1_Model1
## 5   train/test split 11.594601    5 12.375394 Preprocessor1_Model1
## 6   train/test split 10.991874    6 10.508850 Preprocessor1_Model1
## 7   train/test split 13.276337    7 15.591017 Preprocessor1_Model1
## 8   train/test split 12.025331    8 12.399355 Preprocessor1_Model1
## 9   train/test split 10.555396    9 11.103704 Preprocessor1_Model1
## 14  train/test split 11.138368   14 11.775000 Preprocessor1_Model1
## 16  train/test split 11.130612   16 10.032110 Preprocessor1_Model1
## 18  train/test split 11.578473   18 11.997867 Preprocessor1_Model1
## 20  train/test split 11.976586   20 13.163146 Preprocessor1_Model1
## 24  train/test split 11.214763   24 11.705833 Preprocessor1_Model1
## 26  train/test split  8.221750   26  6.911111 Preprocessor1_Model1
## 27  train/test split  9.145834   27  5.928814 Preprocessor1_Model1
## 28  train/test split  9.236475   28 10.492617 Preprocessor1_Model1
## 33  train/test split  8.579986   33  5.528205 Preprocessor1_Model1
## 37  train/test split 10.287879   37  7.465179 Preprocessor1_Model1
## 42  train/test split 11.180045   42 11.249704 Preprocessor1_Model1
## 44  train/test split 11.023703   44 11.714754 Preprocessor1_Model1
## 46  train/test split 10.956379   46 11.153097 Preprocessor1_Model1
## 47  train/test split 10.864757   47 11.186885 Preprocessor1_Model1
## 48  train/test split 10.776668   48 11.058974 Preprocessor1_Model1
## 50  train/test split 10.872170   50 11.259322 Preprocessor1_Model1
## 52  train/test split 11.449672   52 12.119167 Preprocessor1_Model1
## 56  train/test split 10.992161   56 10.685088 Preprocessor1_Model1
## 62  train/test split 10.909094   62 10.164062 Preprocessor1_Model1
## 65  train/test split 16.945436   65 18.677009 Preprocessor1_Model1
## 68  train/test split 11.858360   68  7.600000 Preprocessor1_Model1
## 69  train/test split 12.432114   69  8.217241 Preprocessor1_Model1
## 72  train/test split 12.944475   72  8.082407 Preprocessor1_Model1
## 73  train/test split  9.367895   73  6.695946 Preprocessor1_Model1
## 78  train/test split 17.566192   78 23.160784 Preprocessor1_Model1
## 80  train/test split 10.781196   80  9.030159 Preprocessor1_Model1
## 81  train/test split 13.326296   81 14.213396 Preprocessor1_Model1
## 82  train/test split 13.832038   82 13.929661 Preprocessor1_Model1
## 89  train/test split 13.667197   89 13.709169 Preprocessor1_Model1
## 90  train/test split 12.368442   90  7.120000 Preprocessor1_Model1
## 92  train/test split 10.631456   92 16.694872 Preprocessor1_Model1
## 93  train/test split 12.199328   93  7.166197 Preprocessor1_Model1
## 94  train/test split 11.029984   94 14.300000 Preprocessor1_Model1
## 96  train/test split 12.864128   96 12.765789 Preprocessor1_Model1
## 99  train/test split 11.268991   99 15.281356 Preprocessor1_Model1
## 109 train/test split 10.440387  109  6.936667 Preprocessor1_Model1
## 110 train/test split 14.784894  110 15.815044 Preprocessor1_Model1
## 111 train/test split 13.882877  111  8.644860 Preprocessor1_Model1
## 114 train/test split 14.448754  114 13.346847 Preprocessor1_Model1
## 115 train/test split 13.512649  115 12.305128 Preprocessor1_Model1
## 117 train/test split 13.974295  117 11.304951 Preprocessor1_Model1
## 119 train/test split 13.954762  119 13.742812 Preprocessor1_Model1
## 129 train/test split 11.965519  129 12.265587 Preprocessor1_Model1
## 130 train/test split 10.961074  130  6.767213 Preprocessor1_Model1
## 134 train/test split 11.307722  134  9.078495 Preprocessor1_Model1
## 137 train/test split 11.299203  137 20.648092 Preprocessor1_Model1
## 139 train/test split  8.928850  139  9.693220 Preprocessor1_Model1
## 140 train/test split 10.679921  140 10.683193 Preprocessor1_Model1
## 144 train/test split  7.833687  144  7.184746 Preprocessor1_Model1
## 148 train/test split  8.969778  148  8.218750 Preprocessor1_Model1
## 151 train/test split  7.403119  151  4.318333 Preprocessor1_Model1
## 153 train/test split  7.369298  153  6.679167 Preprocessor1_Model1
## 154 train/test split  7.796318  154  9.112712 Preprocessor1_Model1
## 158 train/test split 10.842527  158 11.921101 Preprocessor1_Model1
## 167 train/test split 11.434373  167 11.286893 Preprocessor1_Model1
## 172 train/test split 11.385793  172 11.368696 Preprocessor1_Model1
## 173 train/test split 12.082615  173 11.276786 Preprocessor1_Model1
## 175 train/test split 12.449249  175 11.484259 Preprocessor1_Model1
## 177 train/test split 12.809236  177 13.529223 Preprocessor1_Model1
## 180 train/test split 11.779915  180 12.436975 Preprocessor1_Model1
## 185 train/test split  8.029144  185  7.555372 Preprocessor1_Model1
## 193 train/test split  8.780377  193  8.552956 Preprocessor1_Model1
## 196 train/test split  9.030007  196 10.567376 Preprocessor1_Model1
## 197 train/test split  7.843719  197  7.967826 Preprocessor1_Model1
## 200 train/test split  8.251498  200  7.545810 Preprocessor1_Model1
## 202 train/test split  8.897461  202  6.196026 Preprocessor1_Model1
## 209 train/test split  8.096943  209  6.931373 Preprocessor1_Model1
## 213 train/test split 12.134977  213 11.916340 Preprocessor1_Model1
## 217 train/test split 11.986866  217 13.743363 Preprocessor1_Model1
## 219 train/test split 12.250170  219 12.713120 Preprocessor1_Model1
## 220 train/test split 12.117263  220 13.073278 Preprocessor1_Model1
## 230 train/test split 12.503752  230 13.492857 Preprocessor1_Model1
## 232 train/test split 12.340790  232 13.163303 Preprocessor1_Model1
## 233 train/test split 11.579852  233 11.893966 Preprocessor1_Model1
## 236 train/test split 12.478164  236 12.475000 Preprocessor1_Model1
## 239 train/test split  8.951312  239  7.912658 Preprocessor1_Model1
## 240 train/test split  9.051523  240  7.718627 Preprocessor1_Model1
## 242 train/test split  8.459810  242  9.050442 Preprocessor1_Model1
## 244 train/test split  7.885751  244  9.720690 Preprocessor1_Model1
## 245 train/test split  8.386360  245 11.701630 Preprocessor1_Model1
## 246 train/test split 11.128594  246  9.181356 Preprocessor1_Model1
## 247 train/test split 11.122543  247 10.487931 Preprocessor1_Model1
## 253 train/test split 12.351795  253 11.905882 Preprocessor1_Model1
## 257 train/test split 12.745895  257 12.045378 Preprocessor1_Model1
## 261 train/test split 11.413522  261 11.291525 Preprocessor1_Model1
## 264 train/test split 11.203691  264 10.850000 Preprocessor1_Model1
## 266 train/test split 11.266463  266  9.360656 Preprocessor1_Model1
## 268 train/test split 10.977451  268 10.090090 Preprocessor1_Model1
## 273 train/test split 11.905121  273 12.410909 Preprocessor1_Model1
## 282 train/test split 11.066927  282 10.361667 Preprocessor1_Model1
## 283 train/test split 11.500954  283 10.709167 Preprocessor1_Model1
## 287 train/test split 12.227520  287 12.198000 Preprocessor1_Model1
## 288 train/test split 12.355649  288 12.535455 Preprocessor1_Model1
## 290 train/test split 11.842134  290 12.255856 Preprocessor1_Model1
## 300 train/test split 12.525279  300 12.227097 Preprocessor1_Model1
## 301 train/test split 12.529161  301 12.875653 Preprocessor1_Model1
## 304 train/test split 11.931802  304 12.184770 Preprocessor1_Model1
## 311 train/test split 11.923590  311 11.327500 Preprocessor1_Model1
## 312 train/test split 11.999382  312 12.376243 Preprocessor1_Model1
## 314 train/test split 12.269814  314 11.598977 Preprocessor1_Model1
## 315 train/test split 12.355680  315 12.266463 Preprocessor1_Model1
## 316 train/test split 12.147766  316 12.533333 Preprocessor1_Model1
## 317 train/test split 12.117849  317 12.453846 Preprocessor1_Model1
## 320 train/test split 10.456559  320 10.389916 Preprocessor1_Model1
## 322 train/test split 11.559052  322 10.997085 Preprocessor1_Model1
## 323 train/test split  9.379590  323 10.244444 Preprocessor1_Model1
## 325 train/test split 10.671116  325 11.435593 Preprocessor1_Model1
## 333 train/test split 10.973709  333 10.277391 Preprocessor1_Model1
## 336 train/test split 11.311779  336 13.464000 Preprocessor1_Model1
## 337 train/test split  9.498917  337  9.269643 Preprocessor1_Model1
## 339 train/test split  9.489572  339  9.154369 Preprocessor1_Model1
## 342 train/test split  9.249663  342  9.754545 Preprocessor1_Model1
## 351 train/test split 12.740704  351 12.074380 Preprocessor1_Model1
## 355 train/test split 11.369456  355 11.982051 Preprocessor1_Model1
## 356 train/test split 12.368210  356 12.016522 Preprocessor1_Model1
## 359 train/test split 11.924352  359 11.491597 Preprocessor1_Model1
## 360 train/test split 12.104992  360 12.231818 Preprocessor1_Model1
## 366 train/test split 12.800158  366 12.015702 Preprocessor1_Model1
## 368 train/test split 12.274325  368 10.459664 Preprocessor1_Model1
## 369 train/test split 12.160504  369 11.991667 Preprocessor1_Model1
## 370 train/test split 11.549569  370 10.552941 Preprocessor1_Model1
## 373 train/test split  9.468023  373  8.764078 Preprocessor1_Model1
## 374 train/test split 10.541419  374  9.251887 Preprocessor1_Model1
## 376 train/test split 10.681639  376  9.660000 Preprocessor1_Model1
## 377 train/test split 10.341299  377 11.648113 Preprocessor1_Model1
## 385 train/test split 10.265530  385 10.584314 Preprocessor1_Model1
## 386 train/test split  9.450040  386 10.312587 Preprocessor1_Model1
## 391 train/test split 11.030732  391 11.709756 Preprocessor1_Model1
## 392 train/test split 12.959014  392 12.553754 Preprocessor1_Model1
## 393 train/test split 11.606602  393 13.223598 Preprocessor1_Model1
## 396 train/test split 11.695543  396 12.508772 Preprocessor1_Model1
## 401 train/test split 12.008370  401 12.531579 Preprocessor1_Model1
## 406 train/test split 10.031061  406  9.045902 Preprocessor1_Model1
## 407 train/test split  9.977414  407  8.713158 Preprocessor1_Model1
## 411 train/test split  9.669654  411 10.768908 Preprocessor1_Model1
## 412 train/test split  9.679414  412 10.809917 Preprocessor1_Model1
## 415 train/test split 10.552043  415 11.157018 Preprocessor1_Model1
## 416 train/test split 10.521534  416 10.668966 Preprocessor1_Model1
## 422 train/test split 11.392446  422  8.935088 Preprocessor1_Model1
## 423 train/test split 10.523122  423  9.898230 Preprocessor1_Model1
## 425 train/test split 10.642095  425 10.572500 Preprocessor1_Model1
## 435 train/test split  9.189394  435  6.522807 Preprocessor1_Model1
## 436 train/test split 11.686182  436 11.400855 Preprocessor1_Model1
## 437 train/test split 10.566695  437  9.594253 Preprocessor1_Model1
## 438 train/test split 11.035571  438 10.895763 Preprocessor1_Model1
## 443 train/test split 12.220456  443 12.864754 Preprocessor1_Model1
## 446 train/test split 10.870423  446 10.958120 Preprocessor1_Model1
## 447 train/test split 11.912376  447 13.398319 Preprocessor1_Model1
## 451 train/test split  7.619610  451  4.744828 Preprocessor1_Model1
## 452 train/test split  9.711107  452  9.490598 Preprocessor1_Model1
## 453 train/test split 10.266137  453  9.447500 Preprocessor1_Model1
## 458 train/test split  9.501819  458 10.176364 Preprocessor1_Model1
## 464 train/test split  8.011770  464  7.807563 Preprocessor1_Model1
## 467 train/test split 10.156474  467  8.405000 Preprocessor1_Model1
## 472 train/test split 11.118928  472 10.332174 Preprocessor1_Model1
## 473 train/test split 11.208216  473  9.804310 Preprocessor1_Model1
## 477 train/test split 11.805113  477 12.421849 Preprocessor1_Model1
## 483 train/test split 11.416404  483 10.109565 Preprocessor1_Model1
## 490 train/test split 12.580958  490 12.939266 Preprocessor1_Model1
## 492 train/test split 12.582553  492 13.363559 Preprocessor1_Model1
## 493 train/test split  8.167537  493  5.367213 Preprocessor1_Model1
## 494 train/test split  8.623729  494  8.893407 Preprocessor1_Model1
## 496 train/test split  8.457296  496  7.913115 Preprocessor1_Model1
## 503 train/test split  7.981780  503  7.850000 Preprocessor1_Model1
## 506 train/test split  8.485352  506  7.191964 Preprocessor1_Model1
## 507 train/test split  8.216410  507 10.190164 Preprocessor1_Model1
## 509 train/test split  9.247557  509  9.181564 Preprocessor1_Model1
## 514 train/test split  8.407079  514  6.783810 Preprocessor1_Model1
## 515 train/test split  8.929157  515  8.215534 Preprocessor1_Model1
## 516 train/test split 10.702471  516  9.284706 Preprocessor1_Model1
## 517 train/test split  8.944930  517  4.521622 Preprocessor1_Model1
## 524 train/test split  9.134682  524  8.712637 Preprocessor1_Model1
## 525 train/test split  9.006789  525  8.195082 Preprocessor1_Model1
## 527 train/test split 10.423975  527 10.230928 Preprocessor1_Model1
## 528 train/test split 10.920195  528 10.771875 Preprocessor1_Model1
## 532 train/test split 12.588972  532 12.334146 Preprocessor1_Model1
## 533 train/test split 12.493131  533 12.749593 Preprocessor1_Model1
## 535 train/test split 12.282266  535 12.957143 Preprocessor1_Model1
## 536 train/test split 12.489367  536 11.622936 Preprocessor1_Model1
## 549 train/test split 11.200066  549 11.166964 Preprocessor1_Model1
## 550 train/test split  8.180823  550  5.978932 Preprocessor1_Model1
## 553 train/test split  7.585172  553 12.436905 Preprocessor1_Model1
## 555 train/test split  7.760762  555  5.072381 Preprocessor1_Model1
## 556 train/test split  6.851392  556  6.211215 Preprocessor1_Model1
## 558 train/test split  7.516901  558  5.879747 Preprocessor1_Model1
## 559 train/test split  7.945094  559  4.509322 Preprocessor1_Model1
## 566 train/test split 10.528274  566 10.692285 Preprocessor1_Model1
## 568 train/test split  7.851414  568  4.298276 Preprocessor1_Model1
## 575 train/test split  9.437031  575  8.150476 Preprocessor1_Model1
## 579 train/test split 11.733323  579 10.692308 Preprocessor1_Model1
## 581 train/test split  8.813473  581  7.913750 Preprocessor1_Model1
## 583 train/test split 10.390521  583 10.957143 Preprocessor1_Model1
## 589 train/test split 11.838594  589 12.348538 Preprocessor1_Model1
## 603 train/test split 11.036499  603 11.136134 Preprocessor1_Model1
## 604 train/test split 12.237979  604 12.395157 Preprocessor1_Model1
## 610 train/test split 11.409665  610 11.761538 Preprocessor1_Model1
## 611 train/test split 11.340007  611 11.853846 Preprocessor1_Model1
## 614 train/test split 10.229308  614 11.199145 Preprocessor1_Model1
## 616 train/test split 11.868213  616 11.393043 Preprocessor1_Model1
## 617 train/test split 10.503418  617  9.153659 Preprocessor1_Model1
## 619 train/test split  8.562517  619  4.574138 Preprocessor1_Model1
## 621 train/test split  8.702588  621  8.327826 Preprocessor1_Model1
## 622 train/test split  8.183801  622  6.516129 Preprocessor1_Model1
## 625 train/test split 12.593328  625 13.789831 Preprocessor1_Model1
## 626 train/test split 12.030848  626 12.796581 Preprocessor1_Model1
## 628 train/test split 12.993594  628 13.222642 Preprocessor1_Model1
## 630 train/test split 12.904467  630 14.039241 Preprocessor1_Model1
## 631 train/test split 13.394581  631 13.638182 Preprocessor1_Model1
## 633 train/test split 12.947408  633 14.566102 Preprocessor1_Model1
## 636 train/test split 13.147157  636 12.441667 Preprocessor1_Model1
## 640 train/test split 13.314857  640 15.162147 Preprocessor1_Model1
## 650 train/test split 12.542211  650 11.372674 Preprocessor1_Model1
## 652 train/test split 12.628939  652 12.129268 Preprocessor1_Model1
## 653 train/test split 12.520420  653 12.345045 Preprocessor1_Model1
## 655 train/test split 12.873746  655 13.135294 Preprocessor1_Model1
## 657 train/test split 12.750993  657 13.359103 Preprocessor1_Model1
## 662 train/test split 13.089190  662 12.450746 Preprocessor1_Model1
## 664 train/test split 12.570371  664 12.967544 Preprocessor1_Model1
## 669 train/test split 11.301653  669 11.555652 Preprocessor1_Model1
## 672 train/test split 10.790222  672  9.997414 Preprocessor1_Model1
## 674 train/test split 10.803055  674 11.084946 Preprocessor1_Model1
## 677 train/test split  9.526234  677  5.221277 Preprocessor1_Model1
## 680 train/test split 10.298783  680  6.915517 Preprocessor1_Model1
## 684 train/test split 10.041420  684  8.422034 Preprocessor1_Model1
## 686 train/test split 10.373691  686  7.311290 Preprocessor1_Model1
## 689 train/test split 10.562329  689  8.355085 Preprocessor1_Model1
## 690 train/test split 10.543988  690  7.737190 Preprocessor1_Model1
## 691 train/test split  9.452967  691  8.283193 Preprocessor1_Model1
## 692 train/test split  9.541189  692  6.715254 Preprocessor1_Model1
## 693 train/test split  9.697435  693  9.746154 Preprocessor1_Model1
## 694 train/test split 11.544522  694 11.427353 Preprocessor1_Model1
## 695 train/test split 13.350405  695 12.981311 Preprocessor1_Model1
## 698 train/test split 12.852496  698 13.518692 Preprocessor1_Model1
## 702 train/test split 12.778366  702 12.412931 Preprocessor1_Model1
## 703 train/test split 13.174036  703 12.533981 Preprocessor1_Model1
## 704 train/test split 12.274148  704 13.896721 Preprocessor1_Model1
## 705 train/test split 11.664298  705 10.821448 Preprocessor1_Model1
## 709 train/test split 13.299823  709 13.870513 Preprocessor1_Model1
## 710 train/test split 11.594639  710 10.724633 Preprocessor1_Model1
## 711 train/test split 11.761115  711 10.077364 Preprocessor1_Model1
## 714 train/test split 12.286132  714 11.761468 Preprocessor1_Model1
## 715 train/test split 12.500283  715 12.267778 Preprocessor1_Model1
## 718 train/test split 13.306949  718 13.346515 Preprocessor1_Model1
## 720 train/test split 13.111013  720 13.094075 Preprocessor1_Model1
## 722 train/test split 11.932302  722 12.380909 Preprocessor1_Model1
## 723 train/test split 11.613684  723 11.020625 Preprocessor1_Model1
## 725 train/test split 13.101147  725 13.402367 Preprocessor1_Model1
## 728 train/test split  9.736534  728 10.678632 Preprocessor1_Model1
## 730 train/test split  9.575450  730  9.027193 Preprocessor1_Model1
## 734 train/test split 10.947530  734 12.163063 Preprocessor1_Model1
## 735 train/test split 11.401383  735 11.410909 Preprocessor1_Model1
## 741 train/test split 11.734060  741 12.383193 Preprocessor1_Model1
## 749 train/test split  7.389263  749  5.252941 Preprocessor1_Model1
## 752 train/test split  8.155078  752  7.740496 Preprocessor1_Model1
## 753 train/test split  8.238650  753  6.715126 Preprocessor1_Model1
## 756 train/test split 11.869730  756 12.578903 Preprocessor1_Model1
## 759 train/test split 10.869823  759 11.167213 Preprocessor1_Model1
## 762 train/test split 11.189223  762 11.487719 Preprocessor1_Model1
## 765 train/test split 10.243987  765  9.272131 Preprocessor1_Model1
## 768 train/test split 10.591787  768 11.859016 Preprocessor1_Model1
## 769 train/test split 10.521802  769 16.151786 Preprocessor1_Model1
## 770 train/test split 11.724622  770 11.776271 Preprocessor1_Model1
## 771 train/test split 11.715460  771 10.778947 Preprocessor1_Model1
## 785 train/test split  9.149385  785  9.704315 Preprocessor1_Model1
## 797 train/test split  9.337306  797  8.654310 Preprocessor1_Model1
## 800 train/test split  9.126558  800  7.759574 Preprocessor1_Model1
## 805 train/test split 11.751686  805 11.301639 Preprocessor1_Model1
## 807 train/test split 11.472187  807 11.229167 Preprocessor1_Model1
## 809 train/test split 11.020510  809 12.063333 Preprocessor1_Model1
## 814 train/test split 10.904728  814 11.498198 Preprocessor1_Model1
## 815 train/test split 11.024425  815 10.589167 Preprocessor1_Model1
## 818 train/test split 11.891652  818 13.664641 Preprocessor1_Model1
## 820 train/test split 11.199264  820 11.701420 Preprocessor1_Model1
## 830 train/test split 12.342700  830 14.158261 Preprocessor1_Model1
## 837 train/test split 12.613581  837 14.201709 Preprocessor1_Model1
## 838 train/test split 12.173873  838 13.716379 Preprocessor1_Model1
## 843 train/test split 12.966254  843 13.856637 Preprocessor1_Model1
## 845 train/test split 11.071637  845 11.751882 Preprocessor1_Model1
## 851 train/test split 10.579716  851 11.835537 Preprocessor1_Model1
## 855 train/test split 11.835620  855 12.694958 Preprocessor1_Model1
## 856 train/test split 11.950616  856 13.318333 Preprocessor1_Model1
## 857 train/test split 11.840416  857 13.058333 Preprocessor1_Model1
## 859 train/test split 10.755876  859 11.272500 Preprocessor1_Model1
## 864 train/test split 11.272888  864 13.546400 Preprocessor1_Model1
## 870 train/test split  8.258503  870  4.500000 Preprocessor1_Model1
## 874 train/test split  6.589595  874  6.173494 Preprocessor1_Model1

Results

The Receiver Operating Characteristic (ROC) curve and Area Under the Curve (AUC) using the roc and auc functions from the pROC package. It assesses the predictive performance of a binary classification model using the actual values in value.y and the predicted probabilities or scores in .pred. The AUC provides a single metric representing the model’s ability to discriminate between the two classes, with a higher AUC indicating better performance.

roc_auc <- roc(cleaned_data$value.y, cleaned_data$.pred)
## Warning in roc.default(cleaned_data$value.y, cleaned_data$.pred): 'response'
## has more than two levels. Consider setting 'levels' explicitly or using
## 'multiclass.roc' instead
## Setting levels: control = 4.298275862, case = 4.318333333
## Setting direction: controls > cases
auc(roc_auc)
## Area under the curve: 1

The function yardstick::metrics() is utilized to compute performance evaluation metrics within the dataset cleaned_data. It is intended to measure the predictive accuracy of a model by comparing the predicted values (.pred) against the actual or ground truth values (value.y). The specific metrics being calulated are rsme, mae, and rsq.

yardstick::metrics(cleaned_data,
                   truth = value.y, estimate = .pred)
## # A tibble: 3 × 3
##   .metric .estimator .estimate
##   <chr>   <chr>          <dbl>
## 1 rmse    standard       1.72 
## 2 rsq     standard       0.610
## 3 mae     standard       1.16
# fit data
RF_final_train_fit <- parsnip::fit(RF_tuned_wflow, data = train_pm)
RF_final_test_fit <- parsnip::fit(RF_tuned_wflow, data = test_pm)

# get predictions on training data
values_pred_train <- predict(RF_final_train_fit, train_pm) %>% 
  bind_cols(train_pm %>% select(value, fips, county, id, zcta, lon, lat)) 

# get predictions on testing data
values_pred_test <- predict(RF_final_test_fit, test_pm) %>% 
  bind_cols(test_pm %>% select(value, fips, county, id, zcta, lon, lat))

# combine
all_pred <- bind_rows(values_pred_test, values_pred_train)
all_pred
## # A tibble: 876 × 8
##    .pred value fips  county     id        zcta    lon   lat
##    <dbl> <dbl> <fct> <chr>      <fct>     <fct> <dbl> <dbl>
##  1  11.5  11.2 1033  Colbert    1033.1002 35660 -87.7  34.8
##  2  11.9  12.4 1055  Etowah     1055.001  35901 -86.0  34.0
##  3  11.1  10.5 1069  Houston    1069.0003 36303 -85.4  31.2
##  4  13.8  15.6 1073  Jefferson  1073.0023 35207 -86.8  33.6
##  5  12.1  12.4 1073  Jefferson  1073.1005 35111 -87.0  33.3
##  6  11.3  11.1 1073  Jefferson  1073.1009 35444 -87.3  33.5
##  7  11.6  11.8 1073  Jefferson  1073.5003 35180 -86.9  33.8
##  8  11.0  10.0 1097  Mobile     1097.0003 36611 -88.1  30.8
##  9  11.9  12.0 1101  Montgomery 1101.0007 36110 -86.3  32.4
## 10  12.7  13.2 1113  Russell    1113.0001 31901 -85.0  32.5
## # ℹ 866 more rows
all_pred %>% group_by(zcta) %>%
  summarize(mean_predictions = mean(.pred), mean_actual = mean(value))
## # A tibble: 842 × 3
##    zcta  mean_predictions mean_actual
##    <fct>            <dbl>       <dbl>
##  1 1022              9.39        9.27
##  2 1103             10.6        10.8 
##  3 1201              9.54        9.96
##  4 1608             10.0        10.0 
##  5 1832              8.95        8.55
##  6 1840              9.29        9.05
##  7 1863              9.15        8.70
##  8 1904              9.47        8.71
##  9 2113             10.5        11.1 
## 10 2119             10.2         9.82
## # ℹ 832 more rows
pred <- ggplot(all_pred, aes(x = lon, y = lat, color = .pred)) +
  geom_jitter() +
  labs(x = "Longitude", y = "Latitude", color = "Predictions") +
  scale_color_continuous(limits = c(0, 25), low = "#deebf7", high = "#3182bd")

truth <- ggplot(all_pred, aes(x = lon, y = lat, color = value)) +
  geom_jitter() +
  labs(x = "Longitude", y = "Latitude", color = "True Value") +
  scale_color_continuous(limits = c(0, 25), low = "#deebf7", high = "#3182bd")

(pred/truth) + plot_annotation(title = "Machine Learning Methods Allow for Prediction of Air Pollution", subtitle = "A random forest model predicts true monitored levels of fine particulate matter (PM 2.5) air pollution based on\ndata about population density and other predictors reasonably well, thus suggesting that we can use similar methods to predict levels\nof pollution in places with poor monitoring",
                  theme = theme(plot.title = element_text(size =12, face = "bold"), 
                                plot.subtitle = element_text(size = 8)))

Conclusion

We used ChatGPT to help us phrase the conclusion.

The study aimed to forecast annual average air pollution levels across US zip code regions, leveraging diverse predictors encompassing population density, urbanization metrics, road density data, alongside satellite pollution and chemical modeling information. The predictive model exhibited promising outcomes, demonstrating high accuracy with a ROC AUC score of 1, indicating impeccable discrimination between the predicted and actual values. The study’s predictive model showcased robust performance, reflected in multiple evaluation metrics. The Root Mean Square Error (RMSE) stood at 1.716, indicating the average deviation of predicted pollution concentrations from actual values, suggesting a relatively low average prediction error. Additionally, the R-squared (RSQ) value of 0.61 denotes a substantial proportion of variance in the pollution levels explained by the model, signifying its capability to capture and account for variability. Furthermore, the Mean Absolute Error (MAE) of 1.159 implies the average absolute deviation between predicted and observed values, further substantiating the model’s accuracy in approximating actual pollution levels at the zip code level. These metrics collectively demonstrate the model’s strong predictive ability and its capacity to effectively leverage the diverse set of predictors for forecasting air pollution concentrations. Due to some installation issues with packages such as rnaturalearth and sf, we decided to plot our predictions and true values using longitude and latitude. By plotting the longitude and latitude, we were able to visualize every zip code in our dataset and compare their predicted with their true value. Overall, our model does a fairly good job predicting pollution in zip codes that aren’t heavily populated. We noticed in higher populated areas such as Los Angeles and New York City, the pollution true values are very high, that our model predicts their pollution rate to be lower than they truly are. Assessing feature importance revealed intriguing insights, notably highlighting ‘state’ as the most influential predictor, followed by ‘CMAQ,’ both substantially more impactful than the other top-ranking variables in the model. This suggests that regional differentiation, potentially tied to state-specific policies or geographically bound factors, heavily influences air pollution levels, emphasizing the significance of localized factors in these predictions.

Extension

For our extension, we chose to explore an additional factor that we thought could impact air pollution: airports. The National Library of Medicine states that “In general, most on-airport studies in the U. S. showed slightly elevated concentrations of gaseous criteria pollutants, specifically carbon monoxide (CO), nitrogen dioxide (NO2), and sulfur dioxide (SO2), even though concentrations are often still below national ambient air quality standards.” [2] Though the concentrations are still below the national standards, this case study is about predicting future pollutant causes and it has been determined that airports show an elevated increase in air pollution in their respective areas. For our extension we will look deeper at these air pollution levels by county to see just how elevated they are in comparison to non-airport counties.

According to our research, the [1] Federal Aviation Administration has determined categories for all commerical airports deeming them one of the following: large hub, medium hub, small hub, or non-hub.

Large Hub: Receives 1 percent or more of the annual U.S. commercial enplanements

Medium Hub: Receives 0.25 to 1.0 percent of the annual U.S. commercial enplanements

Small Hub: Receives 0.05 to 0.25 percent of the annual U.S. commercial enplanements

Nonhub: Receives less than 0.05 percent but more than 10,000 of the annual U.S. commercial enplanement

With these categories in mind, we found it best to just look at the Medium and Large hubs as they would only make up around 1 percent of the U.S’s flights per year. We created our own dataset for this as well and it is incredibly difficult to verify that we accounted for all non-hubs and small-hubs such as privately owned airports and ones not listed. To clarify, the dataset that we created called airports2.csv contains only airports with labels “P-L” and “P-M” meaning Large hub and medium hub respectively.

[1] “Airport Categories.” Airport Categories | Federal Aviation Administration, www.faa.gov/airports/planning_capacity/categories. Accessed 12 Dec. 2023.

[2] Riley, Karie, et al. “A Systematic Review of The Impact of Commercial Aircraft Activity on Air Quality Near Airports.” City and Environment Interactions, U.S. National Library of Medicine, www.ncbi.nlm.nih.gov/pmc/articles/PMC8318113/#:~:text=In%20general%2C%20most%20on%2Dairport,national%20ambient%20air%20quality%20standards. Accessed 12 Dec. 2023.

pm <- pm %>% mutate(has_airport = ifelse(county %in% airports$County, 'Y', 'N'))

hasAP <- ggplot(pm, aes(x = has_airport, y = value)) +
  geom_boxplot() +
  labs(title = "Air Pollution Levels by Airport",
       x = "Has Airport",
       y = "Air Pollution Level") +
  theme_minimal()

hasAP

The chart above shows us that the median pollution level for a county that has an airport is higher than that of a county that doesn’t have an airport. To see exactly how much data we can attribute to having an airport in a county or not, we can make a linear model to give us an R-squared value aka a coefficient of determination.

linear_model <- lm(value ~ has_airport, data = pm)

summary(linear_model)
## 
## Call:
## lm(formula = value ~ has_airport, data = pm)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -7.731 -1.514  0.350  1.571 12.406 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  10.75440    0.09739 110.431   <2e-16 ***
## has_airportY  0.27044    0.21914   1.234    0.217    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.582 on 874 degrees of freedom
## Multiple R-squared:  0.00174,    Adjusted R-squared:  0.0005974 
## F-statistic: 1.523 on 1 and 874 DF,  p-value: 0.2175

Using a linear model, we can determine just how impactful the presence of an airport has on the air pollution levels for the counties listed in our data set. According to the linera model, less than one percent of the variability in the air pollution levels can be explained by whether there is an airport located in a county or not. This is a small R squared value and tells us that not much of the data can be explained but any non-zero value is interesting. Again there are probably other factors as we determined earlier in the case study that had more of an impact on air pollution but it is interesting to see that there is a slight increase in air pollution.

Let’s now take a look at specifically the top five percent of air pollution contributors in the United States to see if the higher producing polluters also have airports in them.

ChatGPT helped us make this graph especially with collecting the top 5 percent

percentile_95 <- quantile(pm$value, 0.95)

pm <- pm %>% mutate(top_5_percent = ifelse(value > percentile_95, 'Top 5%', 'Bottom 95%'))

top_5_pm <- pm %>% filter(top_5_percent == 'Top 5%')

CountyAP <- ggplot(top_5_pm, aes(x = reorder(county, -value), y = value, fill = has_airport)) +
  geom_bar(stat = "identity", position = "dodge") +
  labs(title = "Top 5% of Air Pollution Levels by County and Airport Presence",
       x = "County",
       y = "Air Pollution Level",
       fill = "Has Airport") +
  theme_minimal() + theme(axis.text.x = element_text(angle = 45, hjust = 1))
CountyAP

As we can see here, 9 of the 30 counties had airports. This doesn’t look like much but the math shows us that approximately 30% of the top producing air polluting counties also contain airports in them. 30% is a decent percentage but when further examined the counties associated with each airport are also major metropolitan areas and we determined earlier that areas highly populated areas have a higher pollution levels.

We mentioned earlier that the FAA actually separates each airport by levels determined by the amount of flights out of the total flight count in the united states with the largest contributors to total flights as large hubs and second largest as medium hubs. Even though we determined that airports aren’t a great predictor in the air pollution levels of a specific county, we wanted to see if there was a noticeable difference between the large and medium hubs.

ChatGPT helped us merge data

AVC <- merge(pm, airports, by.x = "county", by.y = "County", all.x = TRUE)

ggplot(AVC, aes(x = has_airport, y = value, fill = FAARating)) +
  geom_boxplot() + labs(title = "Boxplot of Air Pollution Levels by FAA Rating and Airport Presence",
       x = "Has Airport",
       y = "Air Pollution Level",
       fill = "FAA Rating") +
  theme_minimal()

Here we can see that there is a slightly noticeable difference between medium hubs and large hubs but the interesting part is that the medium hubs are higher than the large ones. This tells us that it is even more likely for the size of airports to contribute to air pollution as previously thought because the airports with less flights actually have higher pollution rates. Due to the incredibly minimal gab between the medium and large levels, it seems pretty safe to assume that there are other factors such as state and CMAQ that would be better predictors in the future.

Based on all of the additional data that we have collected, it is reasonable to conclude that airports are not a huge indicator of levels of air pollution but a better indicator of a highly populated county. We found previously that our model does not account for highly populated areas as accurately as we would like but potentially as we saw earlier further exploration with state as our most accurate predictor, potentially combined with airports of the large hub level could add a slightly higher level of certainty. Though our results didn’t indicate a perfect prediction of air pollution levels, it is important to note that in both cases the coefficient of determination was not zero this means that some, though very little, of the data can be explained by air traffic but anything above zero needs to be considered in context. As of right now we think it is safe to continue with air travel and not have to fret too much about fumes from the plane but having a non-zero coefficient of determination tells us there could be some contributions to air pollution from these airports and we as a group believe this could be used as evidence for further research of alternative fuels.